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

Problem 1 :

Solve for r :

6r + 7  =  13 + 7r

Problem 2 :

Solve for x :

-7x - 3x + 2  =  -8x - 8

Problem 3 :

Solve for n :

4n - 40  =  7(-2n + 2)

Problem 4 :

Solve for k :

5(k - 3) - 7(6 - k)  =  24 - 3(8 - k) - 3

Problem 5 :

Solve for x :

3(1 - 3x)  =  2(-4x + 7)

Problem 6 :

Solve for x :

(4x/5) - (7/4)  =  (x/5) + (x/4)

Problem 7 :

Solve for x :

(x - 2)/2 + (x + 10)/9  =  5

Problem 8 :

Solve for x :

(x + 1)(2x + 1)  =  (x + 3)(2x + 3) - 14

Problem 9 :

Solve the following equation :

(1/2)(8y - 6)  =  5y - (y + 3)

Problem 10 :

Solve the following equation :

2(1 - x) + 5x  =  3(x + 1) Problem 1 :

Solve for r :

6r + 7  =  13 + 7r

Solution :

6r + 7  =  13 + 7r

Subtract 6r from each side.

7  =  13 + r

Subtract 13 from each side.

-6  =  r

Problem 2 :

Solve for x :

-7x - 3x + 2  =  -8x - 8

Solution :

-7x - 3x + 2  =  -8x - 8

Simplify.

-10x + 2  =  -8x - 8

2  =  2x - 8

10  =  2x

Divide each side by 2.

5  =  x

Problem 3 :

Solve for n :

4n - 40  =  7(-2n + 2)

Solution :

4n - 40  =  7(-2n + 2)

Use distributive property.

4n - 40  =  -14n + 14

18n - 40  =  14

18n  =  54

Divide each side by 18.

n  =  3

Problem 4 :

Solve for k :

5(k - 3) - 7(6 - k)  =  24 - 3(8 - k) - 3

Solution :

5(k - 3) - 7(6 - k)  =  24 - 3(8 - k) - 3

Use distributive property.

5k - 15 - 42 + 7k  =  24 - 24 + 3k - 3

Simplify.

12k - 57  =  3k - 3

Subtract 3k from each side.

9k - 57  =  -3

9k  =  54

Divide each side by 9.

k  =  6

Problem 5 :

Solve for x :

3(1 - 3x)  =  2(-4x + 7)

Solution :

3(1 - 3x)  =  2(-4x + 7)

Use distributive property.

3 - 9x  =  -8x + 14

3  =  x + 14

Subtract 14 from each side.

-11  =  x

Problem 6 :

Solve for x :

(4x/5) - (7/4)  =  (x/5) + (x/4)

Solution :

(4x/5) - (7/4)  =  (x/5) + (x/4)

The least common multiple of the denominators in the equation is 4 × 5  =  20 and we proceed as follows :

20[4x/5 - 7/4]  =  20[x/5 + x/4]

20(4x/5) - 20(7/4)  =  20(x/5) + 20(x/4)

16x - 35  =  4x + 5x

16x - 35  =  9x

Subtract 9x from each side.

7x - 35  =  0

7x  =  35

Divide each side by 7.

x  =  5

Problem 7 :

Solve for x :

(x - 2)/2 + (x + 10)/9  =  5

Solution :

(x - 2)/2 + (x + 10)/9  =  5

The least common multiple of the denominators in the equation is 2 × 9  =  18 and we proceed as follows :

18[(x - 2)/2 + (x + 10)/9]  =  18(5)

18(x - 2)/2 + 18(x + 10)/9  =  90

9(x - 2) + 2(x + 10)  =  90

9x - 18 + 2x + 20  =  90

11x + 2  =  90

Subtract 2 from each side.

11x  =  88

Divide each side by 11.

x  =  4

Problem 8 :

Solve for x :

(x + 1)(2x + 1)  =  (x + 3)(2x + 3) - 14

Solution :

(x + 1)(2x + 1)  =  (x + 3)(2x + 3) - 14

Simplify.

2x2 + 3x + 1  =  2x2 + 9x + 9 - 14

2x2 + 3x + 1  =  2x2 + 9x - 5

Subtract 2x2 from each side.

3x + 1  =  9x - 5

Subtract 3x from each side.

1  =  6x - 5

6  =  6x

Divide each side by 6.

1  =  x

Problem 9 :

Solve the following equation :

(1/2)(8y - 6)  =  5y - (y + 3)

Solution :

(1/2)(8y - 6)  =  5y - (y + 3)

Simplify both sides.

4y - 3  =  5y - y - 3

4y - 3  =  4y - 3

Subtract 4y from each side.

-3  =  -3

The above result is true. Because the result we get at the last step is true, the given equation has infinitely has many solutions.

Problem 10 :

Solve the following equation :

2(1 - x) + 5x  =  3(x + 1)

Solution :

2(1 - x) + 5x  =  3(x + 1)

Simplify both sides.

2 - 2x + 5x  =  3x + 3

2 + 3x  =  3x + 3

Subtract 3x from each side.

2  =  3

The above result is false. Because 2 is not equal to 3. Because the result we get at the last step is false, the given equation has no solution. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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