First slide

Theory of equations

Question

If $| x - 2 | + | x - 3 | = 7$ , then $x =$

Moderate

A

6
B

$- 1$
C

$6 or - 1$
D

None of these

Solution

Here x = 2 and 3 are the critical points.
when $x < 2, | x - 2 | = - (x - 2), | x - 3 | = - (x - 3)$
$∴ x = - 1$ is a solution.
When $2 \leq x < 3, | x - 2 | = x - 2, | x - 3 | = - (x - 3)$
$∴$ The equation reduces to $x - 2 + 3 - x = 7 \Rightarrow 1 = 7$
$∴$ No solution in this case.
When $x \geq 3,$ the equation reduces to
$x - 2 + x - 3 = 7 \Rightarrow x = 6 > 3$
Hence we get, $x = 6 or - 1$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App