Question

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

Answer 1

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:
`|4x + 8| > 16`
`|4x| > 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.
`4x + 8 > 16` and `4(-1)x + 8 > 16` or `-4x + 8 > 16`
Solving these we obtain:
`4x > 8` ; `x > 2`
and
`-4x > 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.