Question 906047
How to solve inequalities with two absolute value. Is there any easy way? Kindly help me. Here's the question!

Solve the inequality {{{1 - abs(x+1) > abs(2x-1) }}}.
<pre>
In most cases, you have to examine the absolute inequality. That's the easiest way.

Observing the absolute inequality, the ONLY time the left side is POSITIVE is when x = - 1. 
As a result, the right side would equal 3. Thus, the INEQUALITY will be false, as {{{1}}} IS NOT > {{{3}}}. 

Additionally, the left side is zero (0), when x = 0, and x = - 2. As a result, the right side
would equal 1 and 5, respectively. Thus, the INEQUALITY will be false, as {{{0}}} IS NEITHER > {{{1}}}, NOR > {{{5}}}. 

Any other value for x makes the left-side NEGATIVE, while the right side will always be POSITIVE. 

Therefore, NO SOLUTION exists for this absolute inequality.

You could have also subtracted 1 to get: {{{- abs(x + 1) > abs(2x - 1) - 1}}}. It's clear from this that the left side's GREATEST
value (0) occurs when x = - 1, which makes the right side, 2, and the inequality, FALSE. All other values for x
would result in the left side value being negative, or < 0.