Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and...
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![Page 1: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/1.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities 8-8 Solving Radical Equationsand Inequalities
Holt Algebra 2
Warm Up
Lesson Presentation
Lesson Quiz
![Page 2: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/2.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Warm UpSimplify each expression. Assume all variables are positive.
Write each expression in radical form.
1. 2.
3. 4.
5.
6.
![Page 3: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/3.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Solve radical equations and inequalities.
Objective
![Page 4: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/4.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
radical equationradical inequality
Vocabulary
![Page 5: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/5.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
A radical equation contains a variable within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a power.
![Page 6: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/6.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
For a square root, the index of the radical is 2.
Remember!
![Page 7: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/7.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Solve each equation.
Example 1A: Solving Equations Containing One Radical
Subtract 5.
Simplify.
Square both sides.
Solve for x.
Simplify.
Check
![Page 8: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/8.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
7
Example 1B: Solving Equations Containing One Radical
Divide by 7.
Simplify.
Cube both sides.
Solve for x.
Simplify.
Check
Solve each equation.
3
77 5x - 7 84
7=
![Page 9: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/9.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Solve the equation.
Subtract 4.
Simplify.
Square both sides.
Solve for x.
Simplify.
Check
Check It Out! Example 1a
![Page 10: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/10.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Cube both sides.
Solve for x.
Simplify.
Check
Check It Out! Example 1b
Solve the equation.
![Page 11: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/11.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Divide by 6.
Square both sides.
Solve for x.
Simplify.
Check
Check It Out! Example 1c
42 42
Solve the equation.
![Page 12: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/12.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 2: Solving Equations Containing Two Radicals
Square both sides.
Solve
Simplify.
Distribute.
Solve for x.
7x + 2 = 9(3x – 2)
7x + 2 = 27x – 18
20 = 20x
1 = x
![Page 13: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/13.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 2 Continued
Check
3 3
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Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Square both sides.
Solve each equation.
Simplify.
Solve for x.
8x + 6 = 9x
6 = x
Check It Out! Example 2a
Check
![Page 15: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/15.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Cube both sides.
Solve each equation.
Simplify.
Distribute.
x + 6 = 8(x – 1)
Check It Out! Example 2b
x + 6 = 8x – 814 = 7x
2 = x Check
2 2
Solve for x.
![Page 16: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/16.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Raising each side of an equation to an even power may introduce extraneous solutions.
You can use the intersect feature on a graphing calculator to find the point where the two curves intersect.
Helpful Hint
![Page 17: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/17.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Solve .
Example 3: Solving Equations with Extraneous Solutions
Method 1 Use a graphing calculator.
The solution is x = – 1
The graphs intersect in only one point, so there is exactly one solution.
Let Y1 = and Y2 = 5 – x.
![Page 18: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/18.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 3 Continued
Method 2 Use algebra to solve the equation.
Step 1 Solve for x.
Square both sides.
Solve for x.
Factor.
Write in standard form.
Simplify.–3x + 33 = 25 – 10x + x2
0 = x2 – 7x – 8
0 = (x – 8)(x + 1)
x – 8 = 0 or x + 1 = 0
x = 8 or x = –1
![Page 19: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/19.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 3 Continued
Method 2 Use algebra to solve the equation.
Step 2 Use substitution to check for extraneous solutions.
3 –3 6 6 x
Because x = 8 is extraneous, the only solution is x = –1.
![Page 20: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/20.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 1 Use a graphing calculator.
The solution is x = 1.
The graphs intersect in only one point, so there is exactly one solution.
Check It Out! Example 3a
Solve each equation.
Let Y1 = and Y2 = x +3.
![Page 21: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/21.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 2 Use algebra to solve the equation.
Step 1 Solve for x.
Square both sides.
Solve for x.
Factor.
Write in standard form.
Simplify.2x + 14 = x2 + 6x + 9
0 = x2 + 4x – 5
0 = (x + 5)(x – 1)
x + 5 = 0 or x – 1 = 0
x = –5 or x = 1
Check It Out! Example 3a Continued
![Page 22: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/22.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 1 Use algebra to solve the equation.
Step 2 Use substitution to check for extraneous solutions.
4 4 x
Because x = –5 is extraneous, the only solution is x = 1.
Check It Out! Example 3a Continued
2 14 35 5
2 –2
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Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 1 Use a graphing calculator.
Check It Out! Example 3b
Let Y1 = and Y2 = –x +4.
The solutions are x = –4 and x = 3.
The graphs intersect in two points, so there are two solutions.
Solve each equation.
![Page 24: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/24.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 2 Use algebra to solve the equation.
Step 1 Solve for x.
Square both sides.
Solve for x.
Factor.
Write in standard form.
Simplify.–9x + 28 = x2 – 8x + 16
0 = x2 + x – 12
0 = (x + 4)(x – 3)
x + 4 = 0 or x – 3 = 0
x = –4 or x = 3
Check It Out! Example 3b Continued
![Page 25: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/25.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 1 Use algebra to solve the equation.
Step 2 Use substitution to check for extraneous solutions.
Check It Out! Example 3b Continued
![Page 26: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/26.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
To find a power, multiply the exponents.
Remember!
![Page 27: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/27.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 4A: Solving Equations with Rational Exponents
Solve each equation.
(5x + 7) = 3
Cube both sides.
Solve for x.
Factor.
Write in radical form.
Simplify.5x + 7 = 27
5x = 20
x = 4
13
![Page 28: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/28.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 4B: Solving Equations with Rational Exponents
Factor.
Solve for x.
Factor out the GCF, 4.
Raise both sides to the reciprocal power.
Simplify.
2x = (4x + 8)12
(2x)2 = [(4x + 8) ]212
4x2 = 4x + 8
Write in standard form.4x2 – 4x – 8 = 0
4(x2 – x – 2) = 0
4(x – 2)(x + 1) = 0
4 ≠ 0, x – 2 = 0 or x + 1 = 0
x = 2 or x = –1
Step 1 Solve for x.
![Page 29: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/29.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 4B Continued
Step 2 Use substitution to check for extraneous solutions.
2x = (4x + 8)12
2(2) (4(2) + 8)12
4 1612
4 4
2x = (4x + 8)12
2(–1) (4(–1) + 8)12
–2 412
–2 2 x
The only solution is x = 2.
![Page 30: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/30.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Solve each equation.
(x + 5) = 3
Cube both sides.
Solve for x.
Write in radical form.
Simplify.x + 5 = 27
x = 22
13
Check It Out! Example 4a
![Page 31: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/31.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Factor.
Solve for x.
Raise both sides to the reciprocal power.Simplify.
(2x + 15) = x12
[(2x + 15) ]2 = (x)2 12
2x + 15 = x2
Write in standard form.x2 – 2x – 15 = 0
(x – 5)(x + 3) = 0
x – 5 = 0 or x + 3 = 0
x = 5 or x = –3
Step 1 Solve for x.
Check It Out! Example 4b
![Page 32: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/32.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
The only solution is x = 5.
Check It Out! Example 4b Continued
(2(–3) + 15) –312
(–6 + 15) –312
x
(2x + 15) = x12
3 –3
Step 2 Use substitution to check for extraneous solutions.
(2(5) + 15) 512
(2x + 15) = x12
(10 + 15) 512
5 5
![Page 33: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/33.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Solve for x.
Raise both sides to the reciprocal power.
Simplify.
9(x + 6) = 81
[3(x + 6) ]2 = (9)212
Distribute 9.9x + 54 = 81
Check It Out! Example 4c
9x = 27
x = 3
3(x + 6) = 912
Simplify.
![Page 34: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/34.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
A radical inequality is an inequality that contains a variable within a radical. You can solve radical inequalities by graphing or using algebra.
A radical expression with an even index and a negative radicand has no real roots.
Remember!
![Page 35: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/35.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 5: Solving Radical Inequalities
Method 1 Use a graph and a table.
Solve .
On a graphing calculator, let Y1 = and Y2 = 9. The graph of Y1 is at or below the graph of Y2 for values of x between 3 and 21. Notice that Y1 is undefined when < 3.
The solution is 3 ≤ x ≤ 21.
![Page 36: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/36.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 5 Continued
Method 2 Use algebra to solve the inequality.
Step 1 Solve for x.
Subtract 3.
Solve for x.
Simplify.
Square both sides.
2x ≤ 42
x ≤ 21
![Page 37: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/37.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 5 Continued
Method 2 Use algebra to solve the inequality.
Step 2 Consider the radicand.
The radicand cannot be negative.
Solve for x.
2x – 6 ≥ 0
2x ≥ 6
x ≥ 3
The solution of is x ≥ 3 and x ≤ 21, or 3 ≤ x ≤ 21.
![Page 38: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/38.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 1 Use a graph and a table.
Check It Out! Example 5a
On a graphing calculator, let Y1 = and Y2 = 5. The graph of Y1 is at or below the graph of Y2 for values of x between 3 and 12. Notice that Y1 is undefined when < 3.
The solution is 3 ≤ x ≤ 12.
Solve .
![Page 39: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/39.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 2 Use algebra to solve the inequality.
Step 1 Solve for x.
Subtract 2.
Solve for x.
Simplify.
Square both sides.
x – 3 ≤ 9
x ≤ 12
Check It Out! Example 5a Continued
![Page 40: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/40.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 2 Use algebra to solve the inequality.
Step 2 Consider the radicand.
The radicand cannot be negative.
Solve for x.
x – 3 ≥ 0
x ≥ 3
Check It Out! Example 5a Continued
The solution of is x ≥ 3 and x ≤ 12, or 3 ≤ x ≤ 12.
![Page 41: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/41.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 1 Use a graph and a table.
Check It Out! Example 5b
Solve .
The solution is x ≥ –1.
On a graphing calculator, let Y1 = and Y2 = 1. The graph of Y1 is at or above the graph of Y2 for values of x greater than –1. Notice that Y1 is undefined when < –2.
![Page 42: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/42.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 2 Use algebra to solve the inequality.
Step 1 Solve for x.
Solve for x.
Cube both sides.
x + 2 ≥ 1
x ≥ –1
Check It Out! Example 5b Continued
![Page 43: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/43.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Method 2 Use algebra to solve the inequality.
Step 2 Consider the radicand.
The radicand cannot be negative.
Solve for x.
x + 2 ≥ 1
x ≥ –1
Check It Out! Example 5b Continued
The solution of is x ≥ –1.
![Page 44: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/44.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 6: Automobile Application
The time t in seconds that it takes a car to
travel a quarter mile when starting from a
full stop can be estimated by using the
formula , where w is the weight
of the car in pounds and P is the power
delivered by the engine in horsepower. If
the quarter-mile time from a 3590 lb car is
13.4 s, how much power does its engine
deliver? Round to the nearest horsepower.
![Page 45: Holt Algebra 2 8-8 Solving Radical Equations and Inequalities 8-8 Solving Radical Equations and Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation.](https://reader037.fdocuments.in/reader037/viewer/2022110319/56649c765503460f94929f20/html5/thumbnails/45.jpg)
Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Example 6 ContinuedUse the formula to determine the amount of horsepower the 3590 lb car has if it finishes the quarter-mile in 13.4s.
Substitute 13.4 for t and 3590 for w.
Cube both sides.
Solve for P.
Simplify.
2406.104P ≈ 709,548.747
P ≈ 295 The engine delivers a power of about 295 hp.
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Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
A car skids to a stop on a street with a speed limit of 30 mi/h. The skid marks measure 35 ft, and the coefficient of friction was 0.7. Was the car speeding? Explain.
Check It Out! Example 6
Use the formula to determine the greatest possible length of the driver’s skid marks if he was traveling 30 mi/h.
The speed s in miles per hour that a car is traveling when it goes into a skid can be estimated by using the formula s = , where f is the coefficient of friction and d is the length of the skid marks in feet.
30fd
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Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Check It Out! Example 6 Continued
900 = 21d
43 ≈ d
If the car were traveling 30 mi/h, its skid marks would have measured about 43 ft. Because the actual skid marks measure less than 43 ft, the car was not speeding.
Substitute 30 for s and 0.7 for f.
Simplify.
Square both sides.
Simplify.
Solve for d.
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Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Lesson Quiz: Part I
Solve each equation or inequality.
x = 161.
2.
3.
4.
x = –5
x = 14
x = 2
x ≥ 595.
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Holt Algebra 2
8-8 Solving Radical Equationsand Inequalities
Lesson Quiz: Part II
137,258 ft3
6. The radius r in feet of a spherical water tank
can be determined by using the formula ,
where V is the volume of the tank in cubic feet. To the nearest cubic foot, what is the volume of a spherical tank with a radius of 32 ft?