# SOLVING EQUATIONS INVOLVING FRACTIONS WORKSHEET

Problem 1 :

Solve for n :

x/4 + 3  =  x/6 + 7

Problem 2 :

Solve for n :

7n/10 + 3/2  =  3n/5 + 2

Problem 3 :

Solve for k :

k/7 - 6  =  3k/7 + 4

Problem 4 :

Solve for m :

1/3 + 2m  =  m - 3/2

Problem 5 :

Solve for x :

1/2 + 2x/5 - 1  =  x/5 + x

Problem 1 :

Solve for n :

x/4 + 3  =  x/6 + 7

Solution :

Step 1 :

Find the least common multiple of the denominators 4 and 6.

Least common multiple of (4 and 6)  =  12

Step 2 :

x/4 + 3  =  x/6 + 7

Multiply each side of the equation by 12.

12(x/4 + 3)  =  12(x/6 + 7)

Use distributive property.

12(x/4) + 12(3)  =  12(x/6) + 12(7)

3x + 36  =  2x + 84

Subtract 2x from each side.

x + 36  =  84

Subtract 36 from each side.

x  =  48

Problem 2 :

Solve for n :

7n/10 + 3/2  =  3n/5 + 2

Solution :

Step 1 :

Find the least common multiple of the denominators 10, 2 and 5.

Least common multiple of (2, 5 and 10)  =   2  1  1  1

=  10

Step 2 :

Multiply both sides of the equation by 10.

10(7n/10 + 3/2)  =  10(3n/5 + 2)

Use distributive property.

10(7n/10) + 10(3/2)  =  10(3n + 5) + 10(2)

Simplify.

7n + 15  =  6n + 20

Step 3 :

Subtract 6n from each side.

n + 15  =  20

Subtract 15 from each side.

n  =  5

Problem 3 :

Solve for k :

k/7 - 6  =  3k/7 + 4

Solution :

Here, we find only one denominator. That is 7.

Multiply both sides of the equation by 7 to get rid of the denominator 7.

7(k/7 - 6)  =  7(3k/7 + 4)

k - 42  =  3k + 28

Subtract k from each side.

- 42  =  2k + 28

Subtract 28 from each side.

- 70  =  2k

Divide each side by 2.

- 35  =  k

Problem 4 :

Solve for m :

1/3 + 2m  =  m - 3/2

Solution :

Step 1 :

Find the least common multiple of the denominators 2 and 3.

Least common multiple of (2 and 3)  =  6

Step 2 :

Multiply both sides of the equation by 6 to get rid of the denominators 2 and 3.

6(1/3 + 2m)  =  6(m - 3/2)

Use distributive property.

2 + 12m  =  6m - 9

Subtract 6m from each side.

2 + 6m  =  - 9

Subtract 2 from each side.

6m  =  - 11

Divide each side by 6.

m  =  -11/6

Problem 5 :

Solve for x :

1/2 + 2x/5 - 1  =  x/5 + x

Solution :

Step 1 :

Find the least common multiple of the denominators (2 and 5).

Least common multiple of (2 and 5)  =  10

Step 2 :

Multiply both sides of the equation by 10 to get rid of the denominators 2 and 5.

10(1/2 + 2x/5 - 1)  =  10(x/5 + x)

Use distributive property.

5 + 4x - 10  =  2x + 10x

Simplify.

4x - 5  =  12x

Subtract 4x from each side.

- 5  =  8x

Divide each side by 8.

-5/8  =  x

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