CUET CUET Mathematics 2024 - The solution set of the inequality |3 x| ≥|6-3 x| is : | PYQs + Solutions

CUET Mathematics 2024

Algebra

Inequalities

Medium

The solution set of the inequality $|3 x| \geq|6-3 x|$ is :

(-\infty, 1]

[1, \infty)

(-\infty, 1) \cup(1, \infty)

(-\infty,-1) \cup(-1, \infty)

Correct Option: 2

Case 1:

x \geq 2

|6-3x| = 3x-6

The inequality becomes:

|3x| \geq 3x-6

\newline

Since

x \geq 2

, we have

|3x| = 3x

\newline

So:

3x \geq 3x-6

, which is always true when

x \geq 2

Case 2:

0 \leq x < 2

3x \geq 0

and

6-3x > 0

The inequality becomes:

3x \geq 6-3x

\newline

Solving:

6x \geq 6

, so

x \geq 1

\newline

This gives us:

1 \leq x < 2

Case 3:

x < 0

3x < 0

and

6-3x > 0

The inequality becomes:

-3x \geq 6-3x

\newline

Simplifying:

0 \geq 6

(false)

\newline

No solutions here.

Combining all cases, the solution set is:

x \geq 1