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Q. The values of x satisfying $| x - 4 | + | x - 9 | = 5$, is :

Linear Inequalities

Solution:

Consider the given equation $| x - 4 | + | x - 9 | = 5$
$\Rightarrow \:\: \begin{cases} 4 - x + 9 - x = 5 & x \leq 4 \\ x - 4 + 9 - x = 5 & 4 < x \leq 9\\ x - 4 + x - 9 = 5 & x > 9 \end{cases}$
$\Rightarrow \:\: \begin{cases} x = 4 & x \leq 4 \\ 5 = 5 & 4 < x \leq 9\\ x = 9 & x > 9 \end{cases}$
So, $4 \leq x \leq 9$