Solving an inequality with absolute value
- Thread starter CB1101
- Start date
D
Deleted member 4993
Guest
That should mean
(x + 4) ≤ 1 and
-(x+4) ≤ 1 ............edit - I don't know why I had written 4 before _ temporary insanity!!!
Last edited by a moderator:
In general, a function with an absolute value can be expressed as a piecewise function depending on whether the argument is positive or negative.
\(\displaystyle \displaystyle f(x) = \begin{cases}-x + 4 & \text{ if }x \le 4 \\ x - 4 & \text{ if }x > 4 \end{cases} \)
You have to look at the inequality for each piece of the function to find any/all values of \(\displaystyle x\) for which it is true.
Subhotosh Khan, I think you misread "-x + 4" in the OP's post as "x + 4."
\(\displaystyle | -x + 4 \ | \ \le \ 1 \ \ means\)
\(\displaystyle -1 \ \le \ -x + 4 \ ≤ \ 1 \ \ \ \implies\)
\(\displaystyle -1 - 4 \ \le \ -x + 4 - 4 \ \le \ 1 - 4 \ \ \ \implies\)
\(\displaystyle -5 \ \le \ -x \ \le \ -3 \ \ \ \implies\)
\(\displaystyle \dfrac{-5}{-1} \ \ge \ \dfrac{-x}{-1} \ \ge \ \dfrac{-3}{-1} \ \ \ \implies\)
\(\displaystyle 5 \ \ge \ x \ \ge \ 3 \ \ \ \implies\)
\(\displaystyle 3 \ \le \ x \ \le \ 5\)
Thanks, that helped a lot and I was able to solve it along with the other problems like it
