The values of x satisfying |x – 4| + | x –9| =5, is: | MATH - CONDITION FOR COMMON ROOTS, QUADRATIC EXPRESSIONS AND POSITION OF ROOTS | SolveeIt | Solveeit

Today, August 18

Question

The values of x satisfying |x – 4| + | x –9| =5, is:

A

x = 4, 9

B

4 £ x £ 9

C

x £ 4 or x ³ 9

D

None

Answer

4 £ x £ 9

Explanation

Solution

Make cases

case (i) x < 4 we get x = 4 \ No solution

case (ii) 4 £ x < 9 we get 5 = 5 \ x Ī [4, 9)

case (iii) x ³ 9 we get x = 9 \ $\begin{matrix} x = 9 \end{matrix}$

from all cases x Ī [4, 9]