You can
put this solution on YOUR website!Hi. I'm really struggling on the the process required to solve the following absolute value inequality:
absolute value of x squared minus 2 is less than 1
Step 1. Yep, absolute value is a tricky concept. Think of absolute value as a distance measurement. Say you walk five steps forward the distance is 5 steps. Say you walk five steps backward the distance is still 5 steps. That is
.
The absolute value will lead to two inequalities.
Also, when taking the
will always be positive even if x is negative. So when you take the
. Please try to understand this concept.
Step 2. The absolute value leads to two equations given as follows
Equation A where
is positive
Equation B where
is negative. To make it positive we reverse the positions in
to
.
Step 3. Let's start with Equation A
Add 2 to both sides of inequality
Taking the square root to both sides yields
which also leads to two more equations as
for positive x and
for negative x or
where we mulitplied -1 to both sides of the equation and reversed the inequality.
We can combine the two inequalities as
ANSWER:
Step 4. For equation B, let's add
to both sides of the inequality
Take the square root to both sides of the equation.
or
This also leads to two more equations
where x is for positive number and
where x is for negative numbers or
where we multiplied by -1 and reversed the inequality.
ANSWER:
and
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit
http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.
Good luck in your studies!
Respectfully,
Dr J
