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

Add 8x on both sides

-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 

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

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

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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