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Question

Mathematics Question on linear inequalities in one variable

The values of x satisfying ∣x−4∣+∣x−9∣=5| x - 4 | + | x - 9 | = 5, is :

A

x = 4, 9

B

4 ≤\leq x ≤\leq 9

C

x ≤\leq 4 or x ≥ \geq 9

D

none of these

Answer

4 ≤\leq x ≤\leq 9

Explanation

Solution

Consider the given equation ∣x−4∣+∣x−9∣=5 {| x - 4 | + | x - 9 | = 5} ⇒  {4−x+9−x=5x≤4 x−4+9−x=54<x≤9 x−4+x−9=5x>9\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} & {\quad x > 9} \end{cases} ⇒  {x=4x≤4 5=54<x≤9 x=9x>9\Rightarrow \:\: \begin{cases} { x = 4 } & {x \leq 4} \\\ { 5 = 5} & { 4 < x \leq 9}\\\ {x = 9} & {\quad x > 9} \end{cases} So, 4≤x≤9 { 4 \leq x \leq 9}