# SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES WORKSHEETS

## About "Solving equations with variables on both sides worksheets"

Solving equations with variables on both sides worksheets :

Here we are going to see some practice questions on solving equations with variables on both sides.

To solve equations with variables on both sides, we have to bring the variables to the left side of equal sign and the numbers which or not having the variables, that is constants to the right side of equal sign.

## Solving Equations with Variables on Both Sides -Practice questions

(1)  Solve the following equation. Then check the solution.

5t - 9  =  -3t + 7

(2)  Solve the following equation. Then check the solution.

5t - 9  =  -3t + 7

(3)  Solve the following equation. Then check the solution.

(4) Solve the following equation. Then check the solution.

6(r + 2) - 4  =  -10

(5)  Solve the following equation. Then check the solution.

4(2a - 1) = -10(a - 5)

(6)  Solve the following equation. Then check the solution.

## Solving equations with variables on both sides worksheets - Solutions

Question 1 :

Solve the following equation. Then check the solution.

5t - 9  =  -3t + 7

Solution :

5t - 9  =  -3t + 7

In order to get rid of -3t, we have to add 3t on both sides.

5t + 3t - 9  =  -3t + 3t + 7

8t - 9  =  7

In order to get rid of -9, add 9 on both sides

8t - 9 + 9  =  7 + 9

8t  =  16

Divide by 8 on both sides

8t/8  =  16/8

t  =  2

Let us look into the solution of next problem on "Solving equations with variables on both sides worksheets".

Question 2 :

Solve the following equation. Then check the solution.

5t - 9  =  -3t + 7

Solution :

5t - 9  =  -3t + 7

In order to get rid of -3t, we have to add 3t on both sides.

5t + 3t - 9  =  -3t + 3t + 7

8t - 9  =  7

In order to get rid of -9, add 9 on both sides

8t - 9 + 9  =  7 + 9

8t  =  16

Divide by 8 on both sides

8t/8  =  16/8

t  =  2

 L.H.S =  5t - 9=  5(2) - 9=  10 - 9 =  1 R.H.S=  -3t + 7=  -3(2) + 7=  -6 + 7=  1

Hence 2 is the solution.

Question 3 :

Solve the following equation. Then check the solution.

Solution :

(3/4)n + 16  =  2 - (1/8)n

(3/4)n + (1/8)n + 16  =  2 - (1/8)n + (1/8)n

(3n/4) + (n/8)  + 16  =  2

Subtract 16 on both sides

(3n/4) + (n/8)  =  2 - 16

Taking L.C.M on the left side

(3n/4) x (2/2)  +  (n/8)  =  -14

(6n/8) + (n/8)  =  -14

(6n + n)/8  =  -14

7n/8  =  -14

Multiplying by 8 on both sides

7n  =  -14(8)

7n  =  -112

Divide by 7 on both sides

n  =  -112/7  =  -16

 L.H.S  =  (3/4)n + 16  =  (3/4) (-16) + 16  =  3 (-4) + 16  =  -12 + 16  =  4 R.H.S=  2 - (1/8)n  =  2 - (1/8) (-16)  =  2 +  2=  4

Hence -16 is the solution.

Question 4 :

Solve the following equation. Then check the solution.

6(r + 2) - 4  =  -10

Solution :

6(r + 2) - 4  =  -10

Use distributive property,

6r + 12 - 4  =  -10

6r + 8  =  -10

Subtract 8 on both sides,

6r + 8 - 8  =  -10 - 8

6r  =  -18

Divide by 6 on both sides,

6r/6  =  -18/6

r  =  -3

 L.H.S  =  6(r + 2) - 4    =  6(-3 + 2) - 4  =  6 (-1) - 4    =  -6 - 4  =  -10 R.H.S =  -10

Hence -1 is the solution.

Question 5 :

Solve the following equation. Then check the solution.

4(2a - 1) = -10(a - 5)

Solution :

4(2a - 1) = -10(a - 5)

Use distributive property,

8a - 4  =  -10a + 50

8a + 10a - 4  =  -10a + 10a + 50

18a - 4  =  50

18a - 4 + 4  =  50 + 4

18a  =  54

Divide by 18 on both sides,

a  =  54/18

a  =  3

 L.H.S  =  4(2a - 1)  =  4(2⋅3 - 1)  =  4(6 - 1)  =  4(5)  =  20 R.H.S = -10(a - 5)=  -10(3 - 5)=  -10 (-2)  =  20

Hence 3 is the solution.

Question 6 :

Solve the following equation. Then check the solution.

5 -  (1/2) (x - 6)  =  4

Solution :

5 -  (x/2) + 6/2  =  4

5 -  (x/2) + 3  =  4

By simplifying 5 and 3, we get

8 - (x/2)  =  4

Subtract 8 on both sides,

8 - 8 - (x/2)  =  4 - 8

-(x/2)  =  -4

Multiply by -2 on both side,

x  =  8

 L.H.S   =  5 -  (1/2) (8 - 6)  =  5  -  (1/2) (2)  =  5  -  1  =  4 R.H.S  =  4

Hence, the solution is 8.

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