# EQUATIONS WITH DISTRIBUTIVE PROPERTY ON BOTH SIDES WORKSHEET

## About "Equations with distributive property on both sides worksheet"

Equations with distributive property on both sides worksheet :

Worksheet on equations with distributive property on both sides is much useful to the students who would like to practice problems on solving linear equations.

## Equations with distributive property on both sides worksheet - Problems

1.  Solve : 4(x - 3)  =  3(2 + x)

2.  Solve : 7n/10 + 3/2  =  3n/5 + 2

3.  Solve : 0.7n + 0.33  =  0.3n + 0.5

## Equations with distributive property on both sides worksheet - Solution

Problem 1 :

Solve : 4(x - 3)  =  3(2 + x)

Solution :

Step 1 :

Use the Distributive Property.

Distribute 4 to the terms within the parentheses on the left side and 3 to the terms within the parentheses on the right side.

4x - 12  =  6 + 3x

Step 2 :

Use inverse operations to solve the equation.

aaaaaaaaaaaaaaaaaa 4x - 12  =  6 + 3xaaaaaaaaaaaaaaaaaa  aaaaaaaaaaaaaaaaaaaaa + 12  + 12 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa-------------------- aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa 4x         =  18 + 3x aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa-------------------- aaaaaaaaaaaaaaaaa

Subtract 3x from both sides.

aaaaaaaaaaaaaaaaaa 4x          =  18 + 3x aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa- 3x                   - 3x aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa  x          =  18 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaa

Problem 2 :

Solve : 7n/10 + 3/2  =  3n/5 + 2

Solution :

Step 1 :

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

LCM  =  5 x 2 x 1 x 1 x 1

LCM  =  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 + 5(3)  =  2(3n) + 20

7n + 15  =  6n + 20

Step 3 :

Use inverse operations to solve for "n".

Subtract 15 from both sides.

aaaaaaaaaaaaaaaa 7n + 15  =  6n + 20 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - 15           - 15 aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa 7n         =  6n + 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaa

Subtract 6n from both sides.

aaaaaaaaaaaaaaaa 7n         =  6n + 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa -6n            -6n aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa  -------------------- aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa   n         =          5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa  -------------------- aaaaaaaaaaaaaaaa

Problem 3 :

Solve : 0.7n + 0.33  =  0.3n + 0.5

Solution :

Step 1 :

In the second term 0.33 on the left side, we have two digits (more number of digits) after the decimal.

So, multiply both sides of the equation by 10² ( = 100).

100(0.7n + 0.33)  =  100(0.3n + 0.5)

Use the Distributive Property.

100(0.7n) + 100(0.33)  =  100(0.3n) + 100(0.5)

70n + 33  =  30n + 50

Step 2 :

Subtract 33 from both sides.

aaaaaaaaaaaaaaaa 70n + 33  =  30n + 50 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa        - 33             - 33 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ------------------------ aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa 70n          =  30n + 17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ------------------------ aaaaaaaaaaaaaaaa

Subtract 30n from both sides.

aaaaaaaaaaaaaaaa 70n          =  30n + 17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaa  - 30n          = -30n aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa------------------------- aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa   40n          =           17 aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa------------------------- aaaaaaaaaaaaaaaa

Divide both sides by 40.

40n/40  =  17/40

n  =  0.425

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