Question

Solving a Multistep Equation with Fractions
Solve the equation.

3
4
(2a − 6) + 1
2
= 2
5
(3a + 20)

a =

Answer 1

Interpret the equation as (3/4)(2a − 6) + 1/2 = (2/5)(3a + 20).

Compute the left side:
(3/4)(2a − 6) = (3/2)a − 9/2, so
(3/4)(2a − 6) + 1/2 = (3/2)a − 9/2 + 1/2 = (3/2)a − 4.

Right side:
(2/5)(3a + 20) = (6/5)a + 8.

Set equal and solve:
(3/2)a − 4 = (6/5)a + 8
(3/2 − 6/5)a = 12
(15/10 − 12/10)a = 12
(3/10)a = 12
a = 12 · (10/3) = 40.

Check (optional): both sides equal 56 when a = 40.

Answer: a = 40.