# SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES WORKSHEET WITH ANSWER KEY

## About "Solving equations with variables on both sides worksheet with answer key"

Solving equations with variables on both sides worksheet with answer key :

Here we are going to see some practice problems based on the topic variables on both sides.

Solving equations with variables on both sides worksheet with answer key - Practice questions

(1) Solve 6r + 7 = 13 + 7r

(2) Solve  −7x − 3x + 2 = −8x − 8

(3) Solve  4n − 40 = 7(−2n + 2)

(4) Solve  38 + 7k = 8(k + 4)

(5) Solve  3(1 − 3x) = 2(−4x + 7)

(6) Solve 2x + 3 = 5x - 2

(7) Solve  −7x − 3x + 2 = −8x − 8

(8) Solve  −6n − 20 = −2n + 4(1 − 3n)

(9) -8n + 4(1 + 5n) = −6n − 14

(10) Solve 7(5a − 4) − 1 = 14 − 8a

## Solving equations with variables on both sides worksheet with answer key - Solution

Problem 1 :

Solve  6r + 7 = 13 + 7r

Solution :

In order to bring 7r to the left side we have to subtract 7r on both sides.

6r - 7r + 7 = 13 + 7r - 7r

-r + 7 = 13

Now we have to move +7 to the right side. So, we have to subtract 7 on both sides.

-r + 7 - 7 = 13 - 7

-r = 6

r = -6

Problem 2 :

Solve  −7x − 3x + 2 = −8x − 8

Solution :

Now we have to combine the like terms on both sides

-10x + 2 = - 8x - 8

-10x + 8x + 2 = -8x + 8x - 8

-2x + 2 = -8

Subtract by 2 on both sides

-2x + 2 - 2  =  -8 - 2

-2x  =  -10

Divide by -2 on both sides

x = -10/(-2) ==> 5

Problem 3 :

Solve  4n − 40 = 7(−2n + 2)

Solution :

Now we have to distribute 7

4n − 40 = -14n + 14

4n + 14n − 40 = -14n + 14n + 14

18n - 40 = 14

18n - 40 + 40 = 14 + 40

18n = 54

Divide 18 on both sides

n = 54/18 ==> 3

Problem 4 :

Solve  38 + 7k = 8(k + 4)

Solution :

Now we have to distribute 8

38 + 7k = 8k + 32

Subtract 8k n both sides

38 + 7k - 8k = 8k - 8k + 32

38 - k = 32

Subtract 38 on both sides

38 - k - 38 = 32-38

-k = -6

k = 6

Solving equations with variables on both sides worksheet with answer key

Problem 5 :

Solve  3(1 − 3x) = 2(−4x + 7)

Solution :

Now we have to distribute 3 and 2

3 − 9x = −8x + 14

3 − 9x + 8x  = −8x + 8x + 14

3 - x = 14

Subtract 3 on both sides

3 - x - 3 = 14 - 3

-x = 11

x = -11

Problem 6 :

Solve 2x + 3 = 5x - 2

Solution :

In order to bring + 5x to the left side, we have to subtract 5x on both sides.

2x + 3 = 5x - 2

2x - 5x + 3 = 5x - 5x - 2

-3x + 3 = -2

In order to bring +3 to the right side. So, we have to subtract 3 on both sides.

-3x + 3 - 3  = -2 -3

-3x = -5

In order to isolate x we have to divide by -3 on both sides.

-3x/(-3) = -5/(-3)

x = 5/3

Problem 7 :

Solve  −7x − 3x + 2 = −8x − 8

Solution :

−7x − 3x + 2 = −8x − 8

Combining -7x and -3x we will get -10.

-10x + 2 = -8x - 8

Now we have to bring -8x to the left side, so we have to add 8x on both sides.

-10x + 8x + 2 = -8x + 8x - 8

-2x + 2 = -8

subtract 2 on both sides

-2x + 2 - 2 = - 8 - 2

-2x = -10

divide by -2 on both sides

-2x/(-2) = -10/(-2)

x = -5

Problem 8 :

Solve  −6n − 20 = −2n + 4(1 − 3n)

Solution :

Distribute 4 with 1 and -3n

−6n − 20 = −2n + 4(1 − 3n)

−6 n − 20 = −12 n + 4

Add 12 n on both sides

-6n + 12n - 20 = -12n + 12n + 4

6n - 20 = 4

6n - 20 + 20 = 4 + 20

6n = 24

Divide by 6 on both sides

6n/6 = 24/6

n = 4

Problem 9 :

Solve -8n + 4(1 + 5n) = −6n − 14

Solution :

-8n + 4(1 + 5n) = −6n − 14

Distribute 4

-8n + 4 + 20n = −6n − 14

12n + 4 = -6n - 14

12n + 6n + 4 = -6n + 6n - 14

18n + 4 = -14

Subtract 4 on both sides

18n + 4 - 4 = -14 - 4

18n = -18

divide 18 on both sides

n = -18/18

n = -1

Problem 10 :

Solve 7(5a − 4) − 1 = 14 − 8a

Solution :

7(5a − 4) − 1 = 14 − 8a

Distribute 7

35a - 28 - 1 = 14 - 8a

35a - 29 = 14 - 8a

35a + 8a - 29 = 14 - 8a + 8a

43a - 29 = 14

43a - 29 + 29  = 14 + 29

43a = 43

divide 43 on both sides

a = 1

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