**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.

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

**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.

Add 12 to both sides.

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

After having gone through the stuff given above, we hope that the students would have understood "Equations with distributive property on both sides worksheet".

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