Aspire Faculty ID #17255 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

The values of $x$ which satisfied $|3x| \ge |6-3x|$
A. $(0,1]$
B. $[1,4]$
C. $(4,\infty)$
D. $(-1,0)$
E. $(-\infty,0)$

Choose the correct answer from the options given below:

Solution

Given

$|3x| \ge |6-3x|$

$3|x| \ge 3|2-x|$

Divide by 3:

$|x| \ge |2-x|$

Square both sides:

$x^2 \ge (2-x)^2$

$x^2 \ge 4-4x+x^2$

Cancel $x^2$:

$0 \ge 4-4x$

$4x \ge 4$

$x \ge 1$

So solution set:

$[1,\infty)$

From given intervals:

B: $[1,4]$ ✔
C: $(4,\infty)$ ✔

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