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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, $4 \leq x \leq 9$