**Using the distributive property worksheet :**

Worksheet on using the distributive property is much useful to the students who would like to practice problems on solving equations using distributive property.

1. Solve : 4(x - 3) + 2 = 2 + x

2. Solve : 7n/10 + 3/2 = 3n/5 + 2

3. Solve : k/7 - 6 = 3k/7 + 4

**Problem 1 :**

Solve : 4(x - 3) + 2 = 2 + x

**Solution :**

**Step 1 : **

Use the Distributive Property.

Distribute 4 to the terms within the parentheses.

4x - 12 + 2 = 2 + x

Simplify

4x - 10 = 2 + x

**Step 2 : **

Use inverse operations to solve the equation.

Add 10 to both sides.

aaaaaaaaaaaaaaaaaa 4x - 10 = 2 + x aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa + 10 + 10 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa-------------------- aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa 4x = 12 + x aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa-------------------- aaaaaaaaaaaaaaaaa

Subtract x from both sides.

aaaaaaaaaaaaaaaaaa 4x = 12 + x aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa - x - x aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa-------------------- aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa 3x = 12 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa-------------------- aaaaaaaaaaaaaaaaa

Divide both sides by 3.

3x / 3 = 12 / 3

x = 4

**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 : k/7 - 6 = 3k/7 + 4

**Solution :**

**Step 1 : **

Find the least common multiple of the denominators.

Here, we have the same denominator on both sides. That is 7.

So, LCM = 7.

**Step 2 : **

Multiply both sides of the equation by 7.

7(k/7 - 6) = 7(3k/7 + 4)

Use distributive property.

7(k/7) - 7(6) = 7(3k/7) + 7(4)

Simplify.

k - 42 = 3k + 28

**Step 3 :**

Use inverse operations to solve for "k".

Subtract 28 from both sides.

aaaaaaaaaaaaaaaa k - 42 = 3k + 28 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - 28 - 28 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa k - 70 = 3k aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa---------------------- aaaaaaaaaaaaaaaaaa

Subtract k from both sides.

aaaaaaaaaaaaaaaaaaaa k - 70 = 3k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa - k - k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa---------------- aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa -70 = 2k aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa---------------- aaaaaaaaaaaaaaaaaa

Divide both sides by 2.

-70 / 2 = 2k / 2

-35 = k

After having gone through the stuff given above, we hope that the students would have understood "Using the distributive property worksheet".

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