Review Lesson 1: Multi-Step Equations Solutions

Multi-step equations are the foundation of Algebra 2. 
It may be helpful to write or say your Plan for solving an equation if you are not sure how to get started or if the problem requires several steps to solve. 
Clearing fractions by multiplying all terms by the least common denominator, LCD, is a common strategy to use when solving equations. 
Remember to combine like terms carefully and use inverse operations to solve. 
Check your work either by hand or with a calculator.

Example 1

Solve.

$\frac{1}{3} (2 x + 7) = - 4$

Plan

$\cdot (2) + (7) \cdot (\frac{1}{3})$

$\begin{array}{rcl} (3) \frac{1}{3} (2 x + 7) & = & - 4 (3) \\ 2 x + 7 & = & - 12 \\ - 7 - 7 \\ (\frac{1}{2}) 2 x & = & - 19 (\frac{1}{2}) \\ x & = & - \frac{19}{2} \end{array}$

Check
$\begin{array}{rcl} \frac{1}{3} (2 (- \frac{19}{2}) + 7) & = & - 4 \\ \frac{1}{3} (- 19 + 7) & = & - 4 \\ \frac{1}{3} (- 12) & = & - 4 \\ - 4 & = & - 4 \end{array}$

Example 2

Solve.

$\frac{2}{3} x + \frac{2}{5} = \frac{8}{15}$

$\begin{array}{rcl} LCD & = & 15 \\ 15 (\frac{2}{3} x + \frac{2}{5}) & = & \frac{8}{15} (15) \\ 10 x + 6 & = & 8 \\ - 6 - 6 \\ (\frac{1}{10}) 10 x & = & 2 (\frac{1}{10}) \\ x & = & \frac{2}{10} = \frac{1}{5} \end{array}$

Check
$\frac{2}{3} (\frac{1}{5}) + \frac{2}{5} = \frac{8}{15} \frac{2}{15} + \frac{6}{15} = \frac{8}{15} ✓$

Example 3

Solve.

$8 (2 x - 1) + 6 = 11 x + 7 - 4$

$\begin{array}{rcl} 16 x - 8 + 6 & = & 11 x + 3 \\ 16 x - 2 & = & 11 x + 3 \\ - 11 x - 11 x \\ 5 x - 2 & = & 3 \\ + 2 + 2 \\ (\frac{1}{5}) 5 x & = & 5 (\frac{1}{5}) \\ x & = & 1 \end{array}$

Check
$\begin{array}{rcl} 8 (2 (1) - 1) + 6 & = & 11 (1) + 7 - 4 \\ 8 (2 - 1) + 6 & = & 11 + 7 - 4 \\ 8 + 6 & = & 18 - 4 \\ 14 & = & 14 ✓ \end{array}$