# SOLVING MULTI STEP EQUATION WITH VARIABLES ON BOTH SIDES

An equation is a mathematical statement that two expressions have the same value, which are separated by an equal sign, “=”.

To solve multi step equations, we should know about inverse operations.

• Inverse operation of addition (+) is subtraction(-).
• Inverse operation of subtraction(-) is addition(+).
• Inverse operation of multiplication(x) is division (/).
• Inverse operations of division (/) is multiplication (x).

Note :

If it is required, we may use the distributive property.

Solve each of the following equation.

Problem 1 :

-3m - 5 = 5m - 13

Solution :

Subtract 5m from both sides.

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

-8m - 5 = -13

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

-8m = -8

Divide both sides by -8.

m = 1

So, the solution of m is 1.

Problem 2 :

6(y + 7) = 2(y - 3)

Solution :

6(y + 7) = 2(y - 3)

By distributing 6 and 2, we get

6y + 42 = 2y - 6

Subtract 2y from both sides.

6y + 42 - 2y = 2y - 6 - 2y

4y + 42 = -6

Subtract 42 from both sides.

4y + 42 - 42 = -6 - 42

4y = -48

Divide both sides by 4.

4y/4 = -48/4

y = -12

So, the solution of y is -12.

Problem 3 :

10q + 3q + 5 = 2(q - 3)

Solution :

10q + 3q + 5 = 2(q - 3)

10q + 3q + 5 = 2q - 6

13q + 5 = 2q - 6

Subtract 2q from both sides.

13q + 5 - 2q = 2q - 6 - 2q

11q + 5 = -6

Subtract 5 from both sides.

11q + 5 - 5 = -6 - 5

11q = -11

Divide both sides by 11.

11q/11 = -11/11

q = -1

So, the solution of q is -1.

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 :

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

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.

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