Find the values of x for which $| x - 3 | + | x - 4 | = 9$ .

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Solution

Given: $| x - 3 | + | x - 4 | = 9$

Case 1: For $x < 3$

$- (x - 3) - (x - 4) = 9$
$- x + 3 - x + 4 = 9$

$- 2 x + 7 = 9$

$- 2 x = 2$

$\Rightarrow$ $x = - 1$

Case 2: For $3 \leq x < 4$

$(x - 3) - (x - 4) = 9$

$x - 3 - x + 4 = 9$

$1 = 9$ No solution

Case 3: For $x \geq 4$

$x - 3 + x - 4 = 9$

$2 x - 7 = 9$

$2 x = 16$

$\Rightarrow$ $x = 8$

Hence, the values of $x$ are -1 and 8.

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Similar questions

The value of x for which $| x - 3 | + | x - 4 | = 9$ is

\geq

x^{3} + 9 x^{2} - x + 4

x = - 5 + 2 \sqrt{- 4}

x

(\frac{3}{4})^{6} \times (\frac{16}{9})^{5} = (\frac{4}{3})^{x + 2}

3 | x - 8 | = 9

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