Algebra 1 - Solving Equations

One-Step Equations

100

Solve for b:

-7 = b - 3

b = -4

WORK
-7 = b - 3
-7 +3 = b - 3 +3
-4 = b

200

Solve for x:

3x = 6

x = 2

WORK

3x = 6

3x/3 = 6/3

x = 2

300

Solve for x:

5x = 20

(When you see it written 5x that means the same thing as 5*x)

x = 4

WORK

5x = 20

5x/5 = 20/5

x = 4

400

Solve for m:

m - 12 = 28

m = 40

WORK

m - 12 = 28

m -12 +12 = 28 +12

m = 40

500

Solve for p:

-254 = p + 717

p = -971

WORK

-254 = p + 717

-254- 717 = p + 717- 717

p = -971

Two-Step Equations

100

Solve for x:

2x + 3 = 15

(When you see it written 2x that means the same thing as 2*x)

x = 6

WORK

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

(2x)/2 = 12/2

x = 6

200

Solve for a:

2a + 5 = 17

a = 6

WORK

2a + 5 = 17

2a + 5 - 5 = 18 - 5

2a = 12

2a/2 = 12/2

a = 6

300

Solve for t:

-5t + 8 = 3

t = 1

WORK

-5t + 8 = 3

-5t + 8 - 8= 3 - 8

-5t = -5 [which is the same thing as -1t = -5]

-5t/-5=-5/-5

t = 1

400

Solve for x:

4x - 10 = 70

x = 20

WORK

4x - 10 = 70

4x - 10 + 10 = 70 + 10 

4x = 80 

4x/4 = 80/4 

x = 20 

500

Solve for x:

53 = 10x + 3

x = 5 or 5 = x

WORK

53 = 10x + 3

53 - 3 = 10x + 3 - 3

50 = 10x

50/10 = 10x/10

5 = x

Multi-Step Equations

100

Solve for m:

5 = 5m - 23 + 2m

m =4

WORK

5 = 5m - 23 + 2m

5 = 5m + 2m - 23

5 = 7m - 23

5 + 23 = 7m - 23 + 23

28 = 7m

28/7 = 7m/7

4 = m

200

Solve for x:

x + 4 + 2x = 67

x = 21

WORK

(x + 4) + 2x = 67

x + 2x + 4 = 67 

3x + 4 = 67

3x + 4 - 4= 67 - 4

3x = 63

3x/3 = 63/3

x = 21

300

Solve for x:

8(2x - 1) = 24

x = 2

WORK

8(2x - 1) = 24

16x - 8 = 24 [Distributive Property]

16x - 8 + 8 = 24 + 8

16x = 32

16x/(16) = 32/(16)

x = 2

400

Solve for x:

8x + 10 - 5x = 46

x = 113

WORK

8x + 10 - 5x = 46

3x + 10 = 46 

3x + 10 - 10 = 46 -10 

3x = 36

3x/3 = 36/3

x = 12

500

Solve for x:

-14 + 5x - 6 - 2x = 7

x = 24

WORK

-14 + 5x - 6 - 2x = 7

3x - 20 = 7 

3x - 20 + 20 = 7 + 20 

3x = 27 

3x/3 = 27/3

x = 9

Variables on Both Sides

100

Solve for b:

3b - 4 = b + 2

b = 3

WORK

3b - 4 = b + 2

3b - 4 + 4 = b + 2 + 4

3b = b + 6

3b - b = b - b + 6

2b = 6

2b/2 = 6/2

b = 3

200

Solve for x:

5x + 2 = 2x + 14

x = 4

WORK

5x + 2 = 2x + 14

5x + 2 - 2 2x + 14- 2

5x = 2x + 12

5x - 2x = 2x - 2x + 12

3x = 12

3x/3 = 12/3

x = 4

300

Solve for p:

10x = 8x + 48

x = 24

WORK

10x = 8x + 48

10x -8x = 8x -8x + 48

2x = 48 

2x/2 = 48/2

x = 24

400

Solve for x:

10x - 2 = 3x + 33

x = 5

WORK

10x - 2 = 3x + 33 

10x - 3x - 2 = 3x - 3x + 33

7x - 2 + 2 = 33 + 2

7x/7 = 35/7

x = 5

500

Solve for x:

9m - 4 = -3m + 92

NO SOLUTION

m = 8

WORK

9m - 4 = -3m + 92

9m + 3m - 4 = -3m + 3m + 92 

12m - 4 = 92

12m - 4 + 4 = 92 + 4

12m = 96 

12m/12 = 96/12 

m = 8

Expressions

100

Combine like terms 

2c + f + 6c

8c + f

WORK

2c + f + 6c

2c + 6c + f 

8c + f

200

Distribute: 

2(x - 8) 

2x - 16

WORK

2(x - 8)

2x - 16 

300

What is the purpose of solving equations?

The purpose is to find the unknown value of a given variable. (For example x)

400

Distribute: 

7(3x - 13) 

21x - 91

WORK

7(3x - 13)

21x - 91

500

Combine like terms: 

15x + 5 - 10x - 2 + 7 + 23x

28x + 10

WORK

15x + 5 - 10x - 2 + 7 + 23x

15x - 10x + 23x + 5 - 2 + 7

28x + 10