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 $(-\infty, 5)$