# In this lesson, we will look at distributive property and how it can be used to solve algebraic equations.

### Distributive Property

The distributive property of addition and multiplication states that multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products. For example, 3(2 + 4) = (3 2) + (3 4)

The following video shows some examples of the distributive property.

### Solving Equations using Distributive Property

To solve algebra equations using the distributive property, we need to distribute (or multiply) the number with each term in the expression. In that way, the brackets are removed. We can then combine like terms and solve by equivalent equations when necessary.

Remember to apply the following rules for sign multiplication when necessary.

Rules for sign multiplication:

(+) • (+) = (+)

(+) • (–) = (–)

(–) • (+) = (–)

(–) • (–) = (+)

Example:

Solve 3(2x + 5) = 3

Solution:

[3 2x] + [3 5] = 3 (use distributive property)

6x + 15 = 3 (subtract 15 from both sides)

6x = –12 (divide 6 on both sides)

x = –2

Check:

3(2x + 5) = 3 (substitute x = –2 into the original equation)

3((2 • –2) + 5) = 3

Example:

Solve 2x – 2(3x – 2) = 2(x –2) + 20

Solution:

2x – 2(3x – 2) = 2(x –2) + 20
2x – 6x + 4 = 2x – 4 + 20 (use distributive property)
– 4x + 4 = 2x + 16 (combine like terms)
–4x + 4 – 4 –2x = 2x + 16 – 4 –2x (add or subtract on both sides)
–6x = 12 (divide both sides by –6)
x = –2

Check:

2x – 2(3x – 2) = 2(x –2) + 20 (substitute x = –2 into the original equation)

(2 • –2) – 2((3 • –2) –2) = 2(–2 –2) + 20

12 = 12

The following video shows some examples of solving multi-step equation by distributive property.

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