SOLVING MULTI STEP EQUATIONS

Solve each of the following equation.

Problem 1 :

-7x - 5x + 8 = -16

Solution :

-7x - 5x + 8 = -16

-12x + 8 = -16

Subtract 8 from both sides.

-12x + 8 - 8 = -16 - 8

-12x = -24

Divide both sides by -12.

-12x/-12 = -24/-12

x = 2

So, the solution of x is 2.

Problem 2 :

-3m - 5 = 5m - 13

Solution :

Subtract 5m from both sides.

-3m - 5 - 5m = 5m -13 - 5m

-8m - 5 = -13

Add 5 to both sides.

-8m - 5 + 5 = -13 + 5

-8m = -8

Divide both sides by -8.

m = 1

So, the solution of m is 1.

Problem 3 :

3x + 2(x - 5) = 25

Solution :

3x + 2(x - 5) = 25

By distributing 2, we get

3x + 2x - 10 = 25

5x - 10 = 25

Add 10 to both sides.

5x - 10 + 10 = 25 + 10

5x = 35

Divide both sides by 5.

5x/5 = 35/5

x = 7

So, the solution of x is 7.

Problem 4 :

1/3(x + 6) = 2/3(x - 9)

Solution :

1/3(x + 6) = 2/3(x - 9)

By distributing 1/3 and 2/3, we get

(x + 6)/3 = (2x - 18)/3

Multiply by 3 on both sides,

x + 6 = 2x - 18

Subtract 6 from both sides.

x = 2x - 18 - 6

x = 2x - 24

Subtract 2x from both sides.

x - 2x  = 2x - 24 - 2x

-x = -24

x = 24

So, the solution of x is 24.

Problem 5 :

3x + 4x + 5 = 19

Solution :

3x + 4x + 5 = 19

7x + 5 = 19

Subtract 5 from both sides.

7x + 5 - 5 = 19 - 5

7x = 14

Divide both sides by 7.

7x/7 = 14/7

x = 2

So, the solution of x is 2.

Problem 6 :

8k+12=2(k-3)

Solution :

8k + 12 = 2(k - 3)

8k + 12 = 2k - 6

Subtract 2k from both sides.

8k + 12 - 2k = 2k - 6 - 2k

6k + 12 = -6

Add 6 from both sides.

6k + 12 + 6 = -6 + 6

6k + 18 = 0

6k = -18

Divide both sides by 6.

6k/6 = (-18)/6

k = -3

So, the solution of k is -3.

Problem 7 :

5y + 4 - 2y = 9

Solution :

Simplify both sides of the equation.

5y + 4 - 2y = 9

3y + 4 = 9

Subtract 9 from both sides.

3y + 4 - 9 = 9 - 9

3y - 5 = 0

3y = 5

Divide both sides by 3.

3y/3 = 5/3

y = 5/3

So, the solution of y is 5/3.

Problem 8 :

14 = 3(x - 2) + 5

Solution :

14 = 3(x - 2) + 5

14 = 3x - 6 + 5

Subtract 14 from both sides.

14 - 14 = 3x - 6 + 5 - 14

0 = 3x - 15

3x = 15

Divide both sides by 3.

3x/3 = 15/3

x = 5

So, the solution of x is 5.

Problem 9 :

28 = 8x + 12 - 7x

Solution :

28 = 8x + 12 - 7x

28 = x + 12

Subtract 28 from both sides.

28 - 28 = x + 12 - 28

0 = x - 16

x = 16

Problem 10 :

5(1 - 2x) + 8x = 15

Solution :

5(1 - 2x) + 8x = 15

5 - 10x + 8x = 15

5 - 2x = 15

Subtract 15 from both sides.

5 - 2x - 15 = 15 - 15

-10 - 2x = 0

-2x = 10

Divide both sides by 2.

-2x/2 = 10/2

x = -5

Problem 11 :

4y + 7 - y = 19

Solution :

4y + 7 - y = 19

3y + 7 = 19

Subtract 19 from both sides.

3y + 7 - 19 = 19 - 19

3y - 12 = 0

3y = 12

Divide both sides by 3.

3y/3 = 12/3

y = 4

Problem 12 :

-3x - 8 + 4x = 17

Solution :

-3x - 8 + 4x = 17

x - 8 = 17

Subtract 17 from both sides.

x - 8 - 17 = 17 - 17

x - 25 = 0

x = 25