Answer
Interval Notation: $(-∞,\frac{2}{3})∪(2,∞)$
Graph
Work Step by Step
$|6x-8|+3 \gt 7$
By adding $-3$ to both sides of the inequality, isolate the absolute value expression.
$|6x-8|+3- 3 \gt 7-3$
$|6x-8| \gt 4$
Using absolute value inequality property,
$6x - 8 \lt -4$ or $6x-8 \gt 4$
Add $8$ to both sides of the inequalities,
$6x - 8+8 \lt -4+8 $ or $6x-8 +8 \gt 4+8$
$6x \lt 4$ or $6x \gt 12$
Divide by $6$ to both sides of the inequalities,
$x \lt \frac{4}{6}$ or $x \gt \frac{12}{6}$
$x \lt \frac{2}{3}$ or $x \gt 2$
Interval Notation: $(-∞,\frac{2}{3})∪(2,∞)$