Answer
$\left[2,\dfrac{8}{3}\right]$
Work Step by Step
Since $|x|\le c$ (where $c$ is nonnegative) implies $-c\le x\le c$, then the given inequality, $
|3x-7|\le1
$, is equivalent to
\begin{align*}\require{cancel}
-1&\le 3x-7\le1
.\end{align*}
Using the properties of inequality, the inequality above is equivalent to
\begin{align*}
-1+7&\le 3x-7+7\le1+7
\\
6&\le 3x\le8
\\\\
\dfrac{6}{3}&\le \dfrac{\cancel3x}{\cancel3}\le\dfrac{8}{3}
\\\\
2&\le x\le\dfrac{8}{3}
.\end{align*}
Hence, in interval notation, the solution of $
|3x-7|\le1
$ is $\left[2,\dfrac{8}{3}\right]$.
