Question

Solve and graph on a number line.
|3x-8|>7

Answer 1

Solution

To solve $|3x-8|>7, let\, 3x-8=7$

Add 8 to both sides as follows

$3x-8+8=7+8$

$3x=15$

divide by 3 both sides

$\frac{3x} 3=\frac {15} 3$

$x=5$

Again we let $3x-8=-7$

$3x-8+8=-7+8$

$3x=1$

$\frac{3x}3= \frac 13$

$x=\frac 1 3$

since $|3x-8|>7$ is an absolute inequality, so now we have two solutions for x

$x=5$ and

$x=\frac13$

Now the solution on a number line

$x<\frac 1 3$

and

$x>5$