CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Absolute Value Function

If |x-3|+|x-2...

Question

If $| x - 3 | + | x - 2 | = 1$ , then $x \in$

A

[2, 3]

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

(2, 3]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

[2, 3)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

(2, 3)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $[2, 3]$
$| x - 3 | + | x - 2 | = 1$
When $x < 2$
$- 2 x + 5 = 1$
$\Rightarrow x = 2$ No solution

When $2 \leq x < 3$
$1 = 1$ which is true

When $x \geq 3$
$2 x - 5 = 1$
$\Rightarrow x = 3$

$∴ x \in [2, 3]$

Suggest Corrections

thumbs-up

5

Similar questions

| x - 3 | + | x - 2 | = 1

x \in

\frac{| x + 3 | + x}{x + 2} = 1

x \in

x = \frac{1}{2 - \sqrt{3}} t h e n x^{3} - 3 (x - 1) (x + 2) =

\sqrt[3]{3 (\sqrt[3]{x} - \frac{1}{\sqrt[3]{x}})} = 2,

\sqrt[3]{x} + \frac{1}{\sqrt[3]{x}} =

{log}_{3} (x^{3} - x^{2} - x + 1) - {log}_{3} (x - 1) - {log}_{3} (x + 1) = 2

x =

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Absolute Value Function

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon