Answer
$x \lt -8$
Please see image
Work Step by Step
$ 4x+14 \lt 3x+6\qquad$ ...add $-14$ to each side of the inequality.
$ 4x+14-14 \lt 3x+6-14\qquad$ ...simplify.
$ 4x \lt 3x-8\qquad$ ...add $-3x$ to each side of the inequality.
$ 4x-3x \lt 3x-8-3x\qquad$ ...simplify.
$x \lt -8$
The solutions of the given inequality are all real numbers smaller than $-8$.
Smaller numbers are to the left of $-8$.
Use an open dot in the graph to indicate $-8$ is not a solution.
