9.2 – Adding & Subtracting Rational Expressions. Remember adding & subtracting fractions?
Algebra I Solving Equations by Adding or Subtracting
-
Upload
rae-fields -
Category
Documents
-
view
34 -
download
2
description
Transcript of Algebra I Solving Equations by Adding or Subtracting
![Page 1: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/1.jpg)
CONFIDENTIAL 1
Algebra IAlgebra I
Solving Equations by Solving Equations by Adding or SubtractingAdding or Subtracting
![Page 2: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/2.jpg)
CONFIDENTIAL 2
Warm UpWarm Up
1) 4 [ 3 (x + 9 ) + 2]
Simplify:
2) - 3 [ (x - 2) + 5 (x - 2) ]
3) (2b + 5) - ( 8b + 6) + 3 (b - 2)
4) 1 [(10 - g) + (-6 + 3g) ] 2
![Page 3: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/3.jpg)
CONFIDENTIAL 3
Introduction
You can use algebra tiles and an equation mat to model and solve equations. To find the value of the variable, place or remove tiles to get the x-tile by itself on one side of the mat. You must place or remove the same number of yellow
tiles or the same number of red tiles on both sides.
KEY REMEMBER
+ = 1
- = 1+ = x + -+ = 0
![Page 4: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/4.jpg)
CONFIDENTIAL 4
Activity
Use algebra tiles to model and solve x + 6 = 2.
MODEL ALGEBRA
x + 6 = 2
x + 6 + (-6) = 2 + (-6)
Next page
Model x + 6 on the left side of the mat and 2 on the right side of the mat.
Place 6 red tiles on both sides of the mat. This represents adding -6 to both sides of the equation.
![Page 5: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/5.jpg)
CONFIDENTIAL 5
MODEL ALGEBRA
x + 0 = 0 + (-4)
x = -4
Remove zero pairs from both sides of the mat.
One x-tile is equivalent to 4 red tiles.
Use algebra tiles to model and solve each equation.
1) x + 2 = 5
2) 2. x - 7 = 8
![Page 6: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/6.jpg)
CONFIDENTIAL 6
An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.
To find solutions, isolate the variable.
A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side.
Isolate a variable by using inverse operations, which “undo” operations on the variable.
Inverse OperationsOperation Inverse Operation
Addition Subtraction
Subtraction Addition
![Page 7: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/7.jpg)
CONFIDENTIAL 7
Solving Equations by Using Addition
Solve each equation.
a) x - 10 = 4
x - 10 = 4
+ 10 +10
x = 14
Since 10 is subtracted from x, add 10 to both sides to undo the subtraction.
Check
To check your solution, substitute 14 for x in the original equation.
x – 10 = 414 - 10 4
4 4
![Page 8: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/8.jpg)
CONFIDENTIAL 8
b) 2 = m – 1 5 5
2 = m – 15 5
+ 1 + 1 5 5
Since 1 is subtracted from m, 5add 1 to both sides to undo 5the subtraction.
3 = m 5
![Page 9: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/9.jpg)
CONFIDENTIAL 9
Now you try!
1) n - 3.2 = 5.6
2) -6 = k - 6
Solve each equation. Check your answer.
3) 16 = m - 9
![Page 10: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/10.jpg)
CONFIDENTIAL 10
Solving Equations by Using Subtraction
Solve each equation. Check your answer.
a) x + 7 = 9
Since 7 is added to x, subtract 7 from both sides to undo the addition.
x + 7 = 9
- 7 -7
x = 2
Check
To check your solution, substitute 2 for x in the original equation.
x + 7 = 92 + 7 9
9 9
![Page 11: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/11.jpg)
CONFIDENTIAL 11
b) 0.7 = r + 0.4
Since 0.4 is added to r, subtract 0.4 from both sides to undo the addition.
0.7 = r + 0.4
- 0.4 -0.4
0.3 = r
Check
To check your solution, substitute 0.3 for r in the original equation.
0.7 = r + 0.40.7 0.3 + 0.40.7 0.7
![Page 12: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/12.jpg)
CONFIDENTIAL 12
Now you try!
1) d + 1 = 1 2
2) -5 = k + 5
Solve each equation. Check your answer.
3) 6 + t = 14
![Page 13: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/13.jpg)
CONFIDENTIAL 13
Solving Equations by Adding the Opposite
Solve - 8 + b = 2.
- 8 + b = 2 Since -8 is added to b, add 8 to both sides.
+ 8 + 8
b = 10
![Page 14: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/14.jpg)
CONFIDENTIAL 14
Now you try!
1) - 3 + z = 5 4 4
2) -2.3 + m = 7
Solve each equation. Check your answer.
3) -11 + x = 33
![Page 15: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/15.jpg)
CONFIDENTIAL 15
A person’s maximum heart rate is the highest rate, in beats per minute, that the person’s heart should reach.
One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using
this method, write and solve an equation to find the maximum heart rate of a 15-year-old.
Age added to maximum heart rate is 220.Solution:
a + r = 220Write an equation to represent the relationship.
15 + r = 220 Substitute 15 for a. Since 15 is added to r, subtract 15 from both sides to undo the addition.- 15 - 15
r = 205
The maximum heart rate for a 15-year-old is 205 beats per minute. Since age added to maximum heart
rate is 220, the answer should be less than 220. So 205 is a reasonable answer.
![Page 16: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/16.jpg)
CONFIDENTIAL 16
Properties of Equality
WORDS NUMBERS ALGEBRA
Addition Property of EqualityYou can add the same number to both sides of an equation, and the statement will still be
true.
3 = 33 + 2 = 3 + 2
5 = 5
a = ba + c = b + c
Addition Property of EqualityYou can add the same number to both sides of an equation, and the statement will still be
true.
7 = 77 - 5 = 7 - 5
2 = 2
a = ba - c = b - c
![Page 17: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/17.jpg)
CONFIDENTIAL 17
In 1673, the Hope diamond was reduced from its original weight by about 45 carats, resulting in a
diamond weighing about 67 carats. Write and solve an equation to find how many carats the original diamond
weighed. Show that your answer is reasonable.
Now you try!
![Page 18: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/18.jpg)
CONFIDENTIAL 18
Assignments
1) s - 5 = 3
2) 17 = w - 4
3) k - 8 = -7
4) x - 3.9 = 12.4
Factor each trinomial by guess and check:
![Page 19: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/19.jpg)
CONFIDENTIAL 19
5) b + 2 = 2 3
6) 8.4 = y - 4.6
7) 3 = t - 1 8 8
8) t + 5 = -25
9) 9 = s + 9
Factor the trinomial. Check your answer.
![Page 20: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/20.jpg)
CONFIDENTIAL 20
10) Luis deposited $500 into his bank account. He now has $4732. Write and solve an equation to find
how much was in his account before the deposit.
![Page 21: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/21.jpg)
CONFIDENTIAL 21
Let’s review
An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.
To find solutions, isolate the variable.
A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side.
Isolate a variable by using inverse operations, which “undo” operations on the variable.
Inverse OperationsOperation Inverse Operation
Addition Subtraction
Subtraction Addition
![Page 22: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/22.jpg)
CONFIDENTIAL 22
Solving Equations by Using Addition
Solve each equation.
a) x - 10 = 4
x - 10 = 4
+ 10 +10
x = 14
Since 10 is subtracted from x, add 10 to both sides to undo the subtraction.
Check
To check your solution, substitute 14 for x in the original equation.
x – 10 = 414 - 10 4
4 4
review
![Page 23: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/23.jpg)
CONFIDENTIAL 23
b) 2 = m – 1 5 5
2 = m – 15 5
+ 1 + 1 5 5
Since 1 is subtracted from m, 5add 1 to both sides to undo 5the subtraction.
3 = m 5
review
![Page 24: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/24.jpg)
CONFIDENTIAL 24
Solving Equations by Using Subtraction
Solve each equation. Check your answer.
a) x + 7 = 9
Since 7 is added to x, subtract 7 from both sides to undo the addition.
x + 7 = 9
- 7 -7
x = 2
Check
To check your solution, substitute 2 for x in the original equation.
x + 7 = 92 + 7 9
9 9
review
![Page 25: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/25.jpg)
CONFIDENTIAL 25
b) 0.7 = r + 0.4
Since 0.4 is added to r, subtract 0.4 from both sides to undo the addition.
0.7 = r + 0.4
- 0.4 -0.4
0.3 = r
Check
To check your solution, substitute 0.3 for r in the original equation.
0.7 = r + 0.40.7 0.3 + 0.40.7 0.7
review
![Page 26: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/26.jpg)
CONFIDENTIAL 26
review
Solving Equations by Adding the Opposite
Solve - 8 + b = 2.
- 8 + b = 2 Since -8 is added to b, add 8 to both sides.
+ 8 + 8
b = 10
![Page 27: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/27.jpg)
CONFIDENTIAL 27
review
Properties of Equality
WORDS NUMBERS ALGEBRA
Addition Property of EqualityYou can add the same number to both sides of an equation, and the statement will still be
true.
3 = 33 + 2 = 3 + 2
5 = 5
a = ba + c = b + c
Addition Property of EqualityYou can add the same number to both sides of an equation, and the statement will still be
true.
7 = 77 - 5 = 7 - 5
2 = 2
a = ba - c = b - c
![Page 28: Algebra I Solving Equations by Adding or Subtracting](https://reader036.fdocuments.in/reader036/viewer/2022062321/56812ad4550346895d8eb747/html5/thumbnails/28.jpg)
CONFIDENTIAL 28
You did a great job You did a great job today!today!