Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.
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Transcript of Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.
![Page 1: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/1.jpg)
Holt Algebra 1
11-9 Solving Radical Equations
Warm Up 4-22-09Solve each equation.1. 3x +5 = 172. 4x + 1 = 2x – 3 3. 4. (x + 7)(x – 4) = 05. x2 – 11x + 30 = 06. x2 = 2x + 15
4–2
35–7, 4 6, 5
5, –3
![Page 2: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/2.jpg)
Holt Algebra 1
11-9 Solving Radical Equations
Solve radical equations.Objective
![Page 3: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/3.jpg)
Holt Algebra 1
11-9 Solving Radical Equations
radical equationextraneous solution
Vocabulary
![Page 4: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/4.jpg)
Holt Algebra 1
11-9 Solving Radical Equations
A radical equation is an equation that contains a variable within a radical. In this course, you will only study radical equations that contain square roots.
Recall that you use inverse operations to solve equations. For nonnegative numbers, squaring and taking the square root are inverse operations. When an equation contains a variable within a square root, square both sides of the equation to solve.
![Page 5: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/5.jpg)
Holt Algebra 1
11-9 Solving Radical Equations
![Page 6: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/6.jpg)
Holt Algebra 1
11-9 Solving Radical Equations
Directions: Solve the equation. Check your answer.
![Page 7: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/7.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 1
x = 25
55 5
Check
![Page 8: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/8.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 2
100 = 2x50 = x
Check
10 10
![Page 9: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/9.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 3
3x = 1
Check
![Page 10: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/10.jpg)
Holt Algebra 1
11-9 Solving Radical Equations
Some square-root equations do not have the square root isolated. To solve these equations, you may have to isolate the square root before squaring both sides. You can do this by using one or more inverse operations.
![Page 11: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/11.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 4
x = 81Check
9 – 4 55 5
![Page 12: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/12.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 5
x = 46Check
7 7
![Page 13: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/13.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 6
5x + 1 = 165x = 15
x = 3
![Page 14: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/14.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 6 Continued
4 + 6 1010 10
Check
![Page 15: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/15.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 7
Method 1
x = 64
![Page 16: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/16.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 7 Continued
Method 2
x = 64
![Page 17: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/17.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 7 Continued
32 32
Check
![Page 18: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/18.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 8
Method 1
144 = x
![Page 19: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/19.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 8 Continued
Method 2
144 = x
![Page 20: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/20.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 8 Continued
12 12
Check
![Page 21: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/21.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 9
Method 1
x = 100
![Page 22: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/22.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 9 Continued
Method 2
4x = 400x = 100
![Page 23: Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.](https://reader035.fdocuments.in/reader035/viewer/2022070419/56815b69550346895dc95dda/html5/thumbnails/23.jpg)
Holt Algebra 1
11-9 Solving Radical EquationsExample 9 Continued
Check
4 4
4
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Holt Algebra 1
11-9 Solving Radical EquationsLesson Summary
Solve each equation. Check your answer.
1.
3.
2.
4.
36 45
no solution 11