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Solve for x.
6(2x – 8) = 36
Given
12x – 48 = 36
Distributive property
12x – 48 + 48 = 36 + 48
Addition/Subtraction
property of equality
12x + 0 = 84
12x = 84
Combining like terms
12x 84

12 12
Multiplication/Division
property of equality

12 x 84
 
12 1 12
x7
Solve for x.



6(2x – 8) = 36
Simplifying fractions
5x + 6 = 31
5x + 6 = 31
Given
5x + 6 – 6 = 31 – 6
Addition/Subtraction
property of equality
5x + 0 = 25
5x = 25
Combining like terms
5x 25

5
5
Multiplication/Division
property of equality
5 x 25
 
5 1 5
x5
Simplifying fractions
Solve for x.
15x – 10 = -40
Given
15x – 10 + 10= -40 + 10
Addition/Subtraction
property of equality
15x – 0 = -30
15x = -30
Combining like terms
15x 30

15
15
Multiplication/Division
property of equality

15 x 30
 
15 1 15
x  2
Solve for x.

Simplifying fractions
4x + 9 = 16 – 3x
4x + 9 = 16 – 3x
Given
4x + 9 – 9 = 16 – 3x – 9
Addition/Subtraction
property of equality
4x + 0 = 7 – 3x
4x = 7 – 3x
Combining like terms
4x + 3x = 7 – 3x + 3x
Addition/Subtraction
property of equality
7x = 7 – 0
7x = 7
Combining like terms
7x 7

7 7
Multiplication/Division
property of equality


15x – 10 = -40
7 x 7
 
7 1 7
x 1
Simplifying fractions
Solve for x.
5(3x – 20) = -10
Given
15x – 100 = -10
Distributive property
15x – 100 + 100 = -10 + 100
Addition/Subtraction
property of equality
15x + 0 = 90
15x = 90
Combining like terms
15x 90

15 15
Multiplication/Division
property of equality

15 x 90
 
15 1 15
x6
Solve for x.

Simplifying fractions
13x + 20 = -6
13x + 20 = -6
Given
13x + 20 – 20 = -6 – 20
Addition/Subtraction
property of equality
13x + 0 = -26
13x = -26
Combining like terms
13x 26

13
13
Multiplication/Division
property of equality


5(3x – 20) = -10
13 x 26
 
13 1 13
x  2
Simplifying fractions
Solve for x.
2x – 15 – x = 21 + 10x
Given
2x – x – 15 = 21 + 10x
x – 15 = 21 + 10x
Combining like terms
x – 15 + 15 = 21 + 10x + 15
Addition/Subtraction
property of equality
x – 0 = 36 + 10x
x = 36 + 10x
Combining like terms
x – 10x = 36 + 10x – 10x
Addition/Subtraction
property of equality
-9x = 36 + 0x
-9x = 36
Combining like terms
9x 36

9 9
Multiplication/Division
property of equality


2x – 15 – x = 21 + 10x
9 x 36
 
9 1 9
x  4
Simplifying fractions
Write equation in slope-intercept form. 5x + y = 18
5x + y = 18
Given
5x – 5x + y = 18 – 5x
Addition/Subtraction
property of equality
0x + y = 18 – 5x
y = 18 – 5x
Combining like terms
y = -5x + 18
Commutative
property of addition
Write equation in slope-intercept form. -4x + 2y = 8
-4x + 2y = 8
Given
-4x + 4x + 2y = 8 + 4x
Addition/Subtraction
property of equality
0x + 2y = 8 + 4x
2y = 8 + 4x
Combining like terms
2y 8  4x

2
2
Multiplication/Division
property of equality
2 y 8 4x
  
2 1 2 2

y  4  2x
y = 2x + 4

Simplifying fractions
Commutative
property of addition
Write equation in slope-intercept form.
12 – 3y = 30x
Given
12 – 12 – 3y = 30x – 12
Addition/Subtraction
property of equality
0 – 3y = 30x – 12
-3y = 30x – 12
Combining like terms
3y 30x 12

3
3
Multiplication/Division
property of equality
3 y 30x 12
 

3 1 3 3


12 – 3y = 30x
y  10x  4
y = mx + b
m = -10 b = 4
Simplifying fractions
slope-intercept form
m = slope; b = y-intercept
Solve for x.
x + 20 = 35
x + 20 = 35
Given
x + 20 – 20 = 35 – 20
Addition/Subtraction
property of equality
x – 0 = 15
x = 15
Combining like terms
Write equation in slope-intercept form. 3x + 9y = -7
3x + 9y = -7
Given
3x – 3x + 9y = -7 – 3x
Addition/Subtraction
property of equality
0x + 9y = -7 – 3x
9y = -7 – 3x
Combining like terms
9y 7  3x

9
9
Multiplication/Division
property of equality
9 y 7 3x
 

9 1 9
9


Simplifying fractions
1
7
y  x
3
9
Commutative
property of addition
y = mx + b
m = 1 b = 7
slope-intercept form
m = slope; b = y-intercept
3

7 1
y  x
9 3

9
x
6
50
Solve for x.
x
6
50



Given
x 50
50
  6
50 1
1
50 x 6 50
  
50 1 1 1
x  300

Multiplication/Division
property of equality
Simplifying fractions
Write equation in slope-intercept form.
2y + 0.5x= 16
2y + 0.5x = 16
Given
2y + 0.5x – 0.5x = 16 – 0.5x
Addition/Subtraction
property of equality
2y + 0 = 16 – 0.5x
2y = 16 – 0.5x
Combining like terms
2y 16  0.5x

2
2
Multiplication/Division
property of equality
2 y 16 0.5x
  
2 1 2
2

y  8  0.25x
Simplifying fractions
y = -0.25x + 8
Commutative
property of addition
y = mx + b
m = -0.25 b = 8
slope-intercept form
m = slope; b = y-intercept
