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

1 Answer
Jun 4, 2018

Answer:

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.