# Solving two-step linear equations using distributive property: $\;a\left( {x + b} \right) = c$

### Solving two-step linear equations using distributive property: $\;a\left( {x + b} \right) = c$

Distributive property is an algebra property that we use all the time! When you see equations in the form of a(x+b), you can transform them into ax+ab by multiplying the terms inside a set of parentheses. In this section, we will make use of this property to help us solve linear equations.

#### Lessons

• 1.
Solve the equation using model.
a)
$4\left( {x + 1} \right) = 12$

b)
$2\left( {x - 3} \right) = 8$

• 2.
Solve.
a)
$3\left( {x - 9} \right) = 45$

b)
$7\left( {10 + x} \right) = 14$

c)
$- 15 = 3\left( {x - 6} \right)$

d)
$- 22 = 11\left( {x + 13} \right)$

• 3.
John has a round table with a circumference of 314.16 cm, but it is too big for his new home. So, he cut off a 10 cm wide border around the edge.
a)
Write the equation that represents the situation.

b)
What is the circumference of the table now? Round your answer to two decimal places.