Intermediate Algebra, Chapter 2, 2.7 summary exercises, Section 2.7, Problem 48

Evaluate the compound inequality $1 - 2x \geq 5$ and $7 + 3x \geq -2$. Then give the solution in interval notation.

$
\begin{equation}
\begin{aligned}
1 - 2x &\geq 5 && \text{and} & 7 + 3x &\geq -2\\
\\
-2x &\geq 5 - 1 && \text{and} & 3x &\geq - 2 -7
&& \text{Group like terms}\\
\\
-2x &\geq 4 && \text{and} & 3x &\geq -9
&& \text{Combine like terms}\\
\\
x &\leq -2 && \text{and} & x &\geq - 3
&& \text{Divide each side by $-2$ and $3$ then solve for $x$.}
\end{aligned}
\\
\text{Remember that if you divide or multiply negative numbers, the inequality symbol reverses.}
\end{equation}
$

Since the inequalities are joined with $and$, find the intersection of the two solution.
The intersection is shown and is written as $[-3,-2]$