Question

Absolute Value Inequalities, Help?


Can someone explain the steps to solve this? I am completely confused.


Solve: |5x + 2| + 7 < 19
A. x < 2 and x > -14/5
B. x < 2 and x < -14/5
C. x > 2 and x > 14/5
D. x > 2

Answer 1

B

Answer 2

If you subtract 7 from both sides you will have:
\[|5x+2|<12\]

Answer 3

That means that 5x+2 is less than 12 units from 0.
That means that 5x+2 must be between -12 and 12.
And so it must be greater than -12 and less than 12
And so we write:
\[-12<5x+2<12\]

Answer 4

Subtract 2 from all three parts and then divide all three parts by 5:
\[-14<5x<10\]
\[\frac{-14}{5}<x<2\]

Answer 5

So choose A