Solve | -2x + 3| + 8 > 13 and graph the solution?

Question

graph the solution and solve

Answer 1

After a slight manipulation, you'll have |-2x+3| > 5. This should be translated into two statements:

-2x+3 > 5  OR -(-2x+3) > 5  the first one corresponds to the interior of the absolute value already being non-negative, and the second one corresponds to the interior being a negative quantity, so its sign is changed (distributed) to attain absolute value.

 

 

I:  -2x > 2    x < -1  Note reversal of inequality symbol when dividing by coefficient -2

II: 2x - 3 > 5 (after distribution of the - sign); then 2x > 8  so  x > 4.

 

The solution is a disjunction:  all points left of -1 or all points to the right of 4 on the numberline.

 

Interval notation: (-infinity,-1) ∪ (4,infinity)