How do you graph abs(4x +8)> 16?

Jun 4, 2018

Make a table of the points and plot them.

Explanation:

Whether using manual calculations and graph paper of a calculation program, at some point the calculations must be made to generate the points for the graph. The direct solution is:
$| 4 x + 8 | > 16$
$| 4 x | > 8$ ; $| x | > 2$ or, x < -2 AND x > 2

For an absolute value problem the inequality can be split into two parts – one with the expression with a positive variable value, and the other with it as a negative.
$4 x + 8 > 16$ and $4 \left(- 1\right) x + 8 > 16$ or $- 4 x + 8 > 16$
Solving these we obtain:
$4 x > 8$ ; $x > 2$
and
$- 4 x > 8$ ; $x < - 2$ (recall that dividing by a negative reverses an inequality direction).
The solution is thus [-inf, -2) and (2, +inf]. The graph is a dotted line along the x = -2 and x = 2 values, with shading on the left and right sides, clear in the middle.