Answer
$x\displaystyle \lt\frac{1}{2}$
Please see image
Work Step by Step
$ 21x+7\lt 3x+16\qquad$ ...add $-3x$ to each side of the inequality.
$ 21x+7-3x\lt 3x+16-3x\qquad$ ...simplify.
$ 18x+7\lt 16\qquad$ ...add $-7$ to each side of the inequality.
$ 18x+7-7\lt 16-7\qquad$ ...simplify.
$ 18x\lt 9\qquad$ ...divide with $18$.
$ x\displaystyle \lt\frac{9}{18}\qquad$ ...simplify.
$x\displaystyle \lt\frac{1}{2}$
The solutions of the given inequality are all real numbers smaller than $\displaystyle \frac{1}{2}$.
Smaller numbers are to the left of $\displaystyle \frac{1}{2}$.
Use an open dot in the graph to indicate $\displaystyle \frac{1}{2}$ is not a solution.
