Question

Solve and graph the absolute value inequality: |2x + 4| > 8. number line with open circles on negative 6 and 2, shading in between. number line with closed circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 2 and 2, shading going in the opposite directions.

Answer 1

|2x+4| > 8 breaks down into two inequalities: 2x+4 > 8 or 2x+4 < -8

Solving  2x+4 > 8 leads to...
2x+4 > 8
2x+4-4 > 8-4
2x > 4
2x/2 > 4/2
x > 2

Solving 2x+4 < -8 leads to...
2x+4 < -8
2x+4-4 < -8-4
2x < -12
2x/2 < -12/2
x < -6

So either x > 2 or x < -6

You'll have 2 open circles at 2 and -6 on the number line. The shaded region will be the region to the left of -6 and to the right of 2. Basically everything but in between -6 and 2