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  IS NOT > . 



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  IS NEITHER > , NOR > . 



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: . 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. 

RELATED QUESTIONS

Please help me with this problem:

Solve the following absolute value inequalities:... (answered by stanbon,psbhowmick)

Is there any easy way to solve... (answered by josmiceli)

solve each system of inequalities by graphing 

18.
y > 4
y < |x-1|

21. 
yless... (answered by stanbon)

Hello everyone,
I need an easy way to explain to my learners how to solve the following... (answered by josgarithmetic)

Hello and thank you,
My question is..... can you give me step by step instructions on... (answered by bucky)

Solve for x. x!=1 (two answers are required)
According to math_tutor (887), we can solve  (answered by Edwin McCravy)

1. Your friend is taking an algebra class that began one week after ours. Explain to your  (answered by stanbon)

Please help me solve this problem:  Two presidential candidates havde a total of 1882... (answered by checkley77)

I kindly ask someone to go over my answers for my absolute value inequalities test.

1.  (answered by solver91311)