Intermediate Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 56

Evaluate the compound inequality $-5x + 1 \geq 11$ and $ 3x + 5 \geq 26$. Give the solution set in both interval and graph form.


$
\begin{equation}
\begin{aligned}
-5x + 1 - 1 &\geq 11 - 1 && \text{or} & 3x + 5 - 5 &\geq 26 - 5\\
\\
-5x &\geq 10 && \text{or} & 3x &\geq 21\\
\\
\frac{-5x}{-5} &\leq \frac{10}{-5} && \text{or} & \frac{3x}{3} &\geq \frac{21}{3}\\
\\
x &\leq -2 && \text{or} & x &\geq 7
\end{aligned}
\end{equation}
$



The graphs of these two inequalities are






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 $(-\infty, -2] \bigcup [7 ,\infty)$