Question

Find the interval of real numbers which contains x, if x satisfies the condition $|2x-5|<3$

• A. -1 < x < 4
• B. - 4 < x < -1
• C. 1 < x < 4
• D. - 4 < x < 1

Answer 1

The correct option is C 1 < x < 4

$|2x-5|<3$
We know that if $|x|<a$, then
x lies between -a and a
Therefore $|2x-5|<3$ can be written as
$-3<2x-5<3$
Add 5 on each side
-3 + 5 on each side
-3 + 5 < 2x – 5 + 5 < 3 + 5
2 < 2x < 8
Divide by 2 on each side
1 < x < 4
Correct answer is option C.