Intermediate Algebra, Chapter 2, 2.7 summary exercises, Section 2.7, Problem 26

Evaluate the equation $6 - 3(2 - x) < 2(1 + x) + 3$. Then give the solution in set notation.

$
\begin{equation}
\begin{aligned}
6 - 3(2 - x) &< 2( 1+ x) + 3\\
\\
6 - 6 + 3x &< 2 + 2x + 3
&& \text{Apply distributive property}\\
\\
3x &< 5 + 2x
&& \text{Combine like terms}\\
\\
3x - 2x &< 5
&& \text{Simplify}\\
\\
x &< 5
\end{aligned}
\end{equation}
$


Thus, the solution set is $(-\infty, 5)$