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 $\displaystyle \left\{ \frac{11}{3}, 1 \right\}$