Absolute Values on both sides of equation

[ethanarpi]

How do you approach an absolute value question when there are absolute value signs on both sides of the equation:

For example: |b+5| > 2 + |b-3|

I understand that when there is an absolute value on one side you do to cases, one of which is multiplying by negative one. But something like this just confuses me.

Thanks!

[smohit04]

Is b> 0 the answer ... ?

I would prefer to solve such questions graphically, and check what range of b will satisfy the graph.

[jnelson0612]

I think smohit is on the right track here. The answer has to be b>0.

The first thing I would do is assume the case that b is positive and drop the absolute value signs. We get that b+5 > b-1. We can subtract b from both sides and we see that 5 > -1 is always valid. Thus, all positive values of b work.

Next try b=0; does not satisfy the equation. b is not equal to zero.

In the case of b<0, let's see what happens. Our equation is |b+5| > 2 + |b-3|. If I put a negative number in for b, the expression (b+5) gets closer to zero, so its absolute value lessens. The expression (b-3) goes farther away from zero, so its absolute value increases. Since 2 is also added to the right side, the left is never greater than the right. Test out some negative numbers and you can see how this works, and the discrepancy gets even larger as you use a smaller and smaller negative number.

I hope this helps!