Answer
$x \lt -8$
Please see image
![](https://gradesaver.s3.amazonaws.com/uploads/solution/5d50ac63-e360-45ba-af62-8d0b429c95e9/result_image/1562364663.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001816Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1ba9f947af387b4524f1cbb5e61387b64a2c77224a4825fac694d2cf305691ac)
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.