Intermediate Algebra, Chapter 2, 2.7 summary exercises, Section 2.7, Problem 30

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

$
\begin{equation}
\begin{aligned}
5x - (3 + x) &\geq 2 (3x + 1)\\
\\
5x - 3 - x &\geq 6x + 2
&& \text{Apply Distributive Property}\\
\\
4x - 3 &\geq 6x + 2
&& \text{Combine like terms}\\
\\
4x - 6x &\geq 2 + 3
&& \text{Simplify}\\
\\
-2x &\geq 5
&& \text{Evaluate}\\
\\
x &\leq -\frac{5}{2}
&& \text{Divide each side by $-2$ and solve for $x$ and remember that if you divide or multiply negative numbers, the inequality symbol reverses.}
\end{aligned}
\end{equation}
$


Thus, the solution set is $\displaystyle \left( -\infty, -\frac{5}{2} \right]$