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Absolute Value Function

Number of val...

Question

Number of value(s) of $x$ satisfying the equation $- 2 | x - 14 | + 5 = - 6 | x - 15 | - 1$ is

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Solution

$- 2 | x - 14 | + 5 = - 6 | x - 15 | - 1$
$\Rightarrow 3 | x - 15 | - | x - 14 | + 3 = 0$

If $x \geq 15$ ,
$3 x - 45 - x + 14 + 3 = 0 \Rightarrow 2 x = 28 \Rightarrow x = 14$

If $14 \leq x < 15$ ,
$- 3 x + 45 - x + 14 + 3 = 0 \Rightarrow 4 x = 62 \Rightarrow x = 15.5$

If $x < 14$ ,
$- 3 x + 45 + x - 14 + 3 = 0 \Rightarrow 2 x = 34 \Rightarrow x = 17$

Hence, there is no value of $x$ satisfying the given equation.

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