If -x-3-x-4-4- then x-A- 4B- -3C- 7D- 5-2

The correct option is D 52 nbsp;|x+3| |x 4|=4 If x≥ 4, x+3 x+4=4 7=4 Never true. If 3 ≤ x 4, x+3+x 4=4 ⇒ x=52 If x 3 x 3+x 4=4 ⇒ 7=4 Never true. ∴ x= ...

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Standard XI

Mathematics

Inequalities Involving Modulus Function

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

Question

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

4

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- 3

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\frac{5}{2}

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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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Choose the correct options

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Inequalities Involving Modulus Function

Standard XI Mathematics

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If |x+3|−|x−4|=4, then x=

The correct option is C 52 |x+3|−|x−4|=4 If x≥4, x+3−x+4=4 7=4 Never true. If −3≤x<4, x+3+x−4=4 ⇒x=52 If x<−3 −x−3+x−4=4 ⇒−7=4 Never true. ∴x=52

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

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.

$∴ x = \frac{5}{2}$