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

-1 < x < 4

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- 4 < x < -1

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1 < x < 4

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- 4 < x < 1

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Solution

The correct option is C 1 < x < 4
$| 2 x - 5 | < 3$
We know that if $| x | < a$ , then
x lies between -a and a
Therefore $| 2 x - 5 | < 3$ can be written as
$- 3 < 2 x - 5 < 3$
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.

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