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Inequalities Involving Modulus Function

If |x+3|-|x-4...

Question

If $| x + 3 | - | x - 4 | = 4$ , then $x =$

A

4

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B

- 3

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C

\frac{5}{2}

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D

7

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Solution

The correct option is C $\frac{5}{2}$
$| x + 3 | - | x - 4 | = 4$
If $x \geq 4$ ,
$x + 3 - x + 4 = 4$
$7 = 4$ Never true.

If $- 3 \leq x < 4$ ,
$x + 3 + x - 4 = 4 \Rightarrow x = \frac{5}{2}$

If $x < - 3$
$- x - 3 + x - 4 = 4$
$\Rightarrow - 7 = 4$ Never true.

$∴ x = \frac{5}{2}$

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Inequalities Involving Modulus Function

Standard XI Mathematics

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