Intermediate Algebra, Chapter 2, 2.7 summary exercises, Section 2.7, Problem 10

Evaluate the equation $|3x - 7| - 4 = 0$. Then give the solution in set notation.

$
\begin{equation}
\begin{aligned}
|3x - 7| - 4 &= 0\\
\\
|3x - 7| &= 4 && \text{Add 4 on each side}
\end{aligned}
\end{equation}
$


By using the property of Absolute value, we have

$
\begin{equation}
\begin{aligned}
3x - 7 &= 4 && \text{and} & 3x - 7 &= -4\\
\\
3x &= 11 && \text{and} & 3x & = 3 && \text{Add 7 on each side}\\
\\
x &= \frac{11}{3} && \text{and} & x &= 1 && \text{Divide each side by $3$ and solve for $x$.}
\end{aligned}
\end{equation}
$



Thus, the solution set is $\displaystyle \left\{ \frac{11}{3}, 1 \right\}$