CPM Homework Help : ACC7 Problem 6-49

When Ms. Shreve solved an equation in class, she checked her solution and it did not make the equation true! Examine her work below and find her mistake. Then find the correct solution.

$\begin{aligned} 5 ( 2 x - 1 ) - 3 x &= 5 x + 9 \\ 10 x - 5 - 3 x &= 5 x + 9 \\ 7 x - 5 &= 5 x + 9 \\ 12 x &= 4 \\ x &= \tfrac { 1 } { 3 } \end{aligned}$

Hint 1:

Go through her solution step by step and check for mistakes.

Hint 2:

She combined like terms from opposite sides of the equation.

$\begin{align*} 5 ( 2 x - 1 ) - 3 x &= 5 x + 9 \\10 x - 5 - 3 x &= 5 x + 9 \\\boxed{7 x} - 5 &= \boxed{5 x} + 9 \\ \boxed{12 x} &= 4 \\x &= \tfrac { 1 } { 3 } \end{align*}$

Hint 3:

Create your own solution, correcting this mistake, and solve for $x$ .