Answer
$-4\lt x\le 1$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
x-10\lt5x+6\le x+10
.$ 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}
x-10\lt5x+6\le x+10
\\\\
x-10-x\lt5x+6-x\le x+10-x
\\\\
-10\lt4x+6\le 10
\\\\
-10-6\lt4x+6-6\le 10-6
\\\\
-16\lt4x\le 4
\\\\
\dfrac{-16}{4}\lt\dfrac{4x}{4}\le \dfrac{4}{4}
\\\\
-4\lt x\le 1
.\end{array}
The graph consists of all points from $-4$ (exclusive) to $1$ (inclusive).
