Intermediate Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 42

Evaluate the inequality $\displaystyle \frac{5}{3} ( x - 2) + \frac{2}{5} (x + 1) > 1$. Express the solution set in interval form.


$
\begin{equation}
\begin{aligned}
\frac{5}{3}x - \frac{10}{3} + \frac{2}{5} x + \frac{2}{5} &> 1
&& \text{Apply Distributive Property}\\
\\
\frac{31}{15} x - \frac{44}{15} &> 1
&& \text{Combine like terms then get the LCD}\\
\\
\frac{31}{15} x &> \frac{59}{15}
&& \text{Simplify}\\
\\
x &> \frac{59}{15}\left( \frac{15}{31} \right)
&& \text{Multiply each side by the reciprocal of $\displaystyle \frac{31}{15}$ to solve for } x\\
\\
x &> \frac{59}{31}
\end{aligned}
\end{equation}
$

Thus, the solution set in interval form is $\left( \frac{59}{31}, \infty \right)$