Intermediate Algebra, Chapter 2, 2.7 summary exercises, Section 2.7, Problem 12

Evaluate the inequality $|5x - 8| + 9 \geq 7$. Then give the solution in interval notation.

$\begin{equation} \begin{aligned} |5x - 8| + 9 &\geq 0\\ \\ |5x - 8| &\geq -2 && \text{Subtract 9 on each side} \end{aligned} \end{equation}$


By using the property of Absolute value, we have

$\begin{equation} \begin{aligned} 5x - 8 &\geq -2 && \text{or} & 5x - 8 &\leq - (-2)\\ \\ 5x - 8 &\geq -2 && \text{or} & 5x - 8 &\leq 2\\ \\ 5x &\geq 6 && \text{or} & 5x &\leq 10 && \text{Add 8 on each side}\\ \\ x &\geq \frac{6}{5} && \text{or} & x &\leq 2 && \text{Divide each side by $5$ and solve for $x$.} \end{aligned} \end{equation}$



Since the inequalities are joined with $or$, find the union of two union of the two solution. The union is shown and is
written as $(-\infty,\infty)$