Kenneth S. answered • 03/16/16
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This type of inequality (absolute value > a constant) is called a DISJUNCTION.
It should be translated into two statements, connected with the word OR:
-4X+3 > 13 or -4x+3 < -13
-4x > 10 or -4x < -16. Now we'll have to divide by -4, and remember to reverse the direction of the inequality symbols.
x < -5/2 or x > 4.
On the numberline, we have <<<<<<<<<<<<(-2.5)...................(4)>>>>>>>>>>>>>>>>>>>
or in interval notation the solution is (-infinity,-2.5) ∪ (4,infinity)
David W.
if |x| > 13
then either
x > 13 or (-x) > 13
For this problem:
if l-4x+3l > 13
then either
(-4x+3) > 13 or (-(-4x+3)) > 13
which is, either
(-4x+3) > 13 or (-4x+3) < 13 [note: multiply by (-1) reverses the sense of the inequality)
03/16/16