Answer
$-\dfrac{1}{8}\lt x \lt \dfrac{1}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
3x\lt4-5x\lt5+3x
.$ Then graph the solution set.
In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given is equivalent to
\begin{array}{l}\require{cancel}
3x\lt4-5x\lt5+3x
\\\\
3x-3x\lt4-5x-3x\lt5+3x-3x
\\\\
0\lt4-8x\lt5
\\\\
0-4\lt4-8x-4\lt5-4
\\\\
-4\lt-8x\lt1
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-4\lt-8x\lt1
\\\\
\dfrac{-4}{-8}\lt\dfrac{-8x}{-8}\lt\dfrac{1}{-8}
\\\\
\dfrac{1}{2}\gt x \gt -\dfrac{1}{8}
\\\\
-\dfrac{1}{8}\lt x \lt \dfrac{1}{2}
.\end{array}
The graph consists of all points from $-\dfrac{1}{8}$ (exclusive) to $\dfrac{1}{2}$ (exclusive).
