NOTES:

|7| is 7

|-7| is 7

Absolute value is ALWAYS a positive number because it represents the distance from zero on a number line

2|x|+1=5

2|x|+1-1=5-1

2|x|=4

|x|=2 by dividing by 2

which means x is 2 OR -2.

This is impossible. |x|=-5. Absolute value cannot be negative. If you get such an answer indicate it does not have a solution by putting -1 in BOTH solution boxes. This is not the answer, it simply indicates you know it is not possible.

What about this?

5|2x+1|+6=41 5|2x+1|=35 (subtract 6 from both sides) |2x+1|=7 (divide by 5) 2x+1=7 OR 2x+1=-7 (absolute value!) 2x=6 OR 2x=-8 (subtract 1 from both sides) x=3 OR x=-4 (divide by 2)