Uses of Distributive Property

Key Concepts

• Solve equations using the distributive property

• Solve equations using distributing a negative number

• Solve equations using distributing a rational number

5.3 Solve Equations Using the Distributive Property 

Distributive property: 

The distributive property involves the use of parentheses and explains how to multiply a number or term outside the parentheses with the numbers or terms inside the parentheses. 

Steps for Solving Algebra Equations using distributive property: 

• If you see parenthesis with more than one term inside, then distribute first! 
• Rewrite your equations with like terms together. Take the sign in front of each term. 

• Combine like terms. 
• Continue solving the one or two-step equations. 

Example: 

5.3.1. Solve Equations Using the Distributive Property 

Example 1: 

Solve equation using the distributive property. 

2(5x – 3) = 14 

Sol: 

2(5x – 3) = 14 

 (2 × 5x) – (2 × 3) =14 

10x – 6 =14 

10x – 6 + 6 = 14 + 6 Add 6 to both sides 

10x = 20 Divide 10 by each side  

x = 2 

5.3.2. Solve Equations Using Distributing a Negative Number 

Negative Number: 

A negative number represents the opposite. In the real number system, a negative number is a number that is less than zero. 

Example 1: 

Use the distributive property to solve the equation. 

–6(m – 3) = –30 

Sol: 

–6(m – 3) = –30 

–6m + 18 = –30 

–6m + 18 – 18 = –30 – 18 Subtract 18 from both sides 

–6m = –48 Divide each side by 6  

m = 8 

5.3.3. Solve Equations Using Distributing a Rational number 

Rational number: 

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. 

Example 1: 

1818

  (p + 24) =9 

Sol: 

1818

  (p + 24) =9 

1818

p +

1818 (24) =9 

18

P + 3 =9 

18

P + 3 – 3 =9 – 3 Subtract 3 from both sides.    

18

P = 6 

( 8 1)1 8( 8 1)1 8

P = 6 (

8  1)8  1)

P = 48 

Exercise:

1. Solve the equation using distributive property – 4(x + 3) = 8.

2. A gym charges a $50 activation fee and $17 per month for a membership. If you spend $356, for how many months do you have a gym membership?

3. Solve the equation 3x + 2(2x -1) = 33.

4. Use the distributive property to solve the equation 6(x + 3) = 48.

5. Solve the equation -2 (x – 2) = 4. 3

6. Solve the equation using distributive property -106 = -2(5 + 6x)

7. 3(x + 3) = -15

8. 0.4(x – 0.45) = 9.2

9. A family of 7 bought tickets to the circus. Each family member also bought a souvenir that cost $6. The total amount they spent was $147. How much did one ticket cost?

10. Use the distributive property to solve the equation -2(p – 200) =42.

Concept Map

What have we learned:

■Understand the distributive property

■ Understand how to solve equations using the distributive property

■ Solve equations using distributing a negative number

■ Solve equations using distributing a rational number