**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

**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

Add 8x on both sides

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

-2x = -8

Divide by -2 on both sides

x = -8/(-2) ==> 4

**Problem 3 :**

Solve 4n − 40 = 7(−2n + 2)

**Solution :**

Now we have to distribute 7

4n − 40 = -14n + 14

Add 14n on both sides

4n + 14n − 40 = -14n + 14n + 14

18n - 40 = 14

Add 40 on both sides

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

Add 8x on both sides

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

Since -3 is multiplied by x, 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

Add 20 on both sides

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

Add 6n on both sides

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

Add 8a on both sides

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

43a - 29 = 14

Add 29 on both sides

43a - 29 + 29 = 14 + 29

43a = 43

divide 43 on both sides

a = 1

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