Question

HELPPPPP :Expressions: Multiple choice: picture provided. With questions and answer choices. USA test prep question

Answer 1

Option B:

$x=\pm 2\frac{1}{2}$

Solution:

Given expression:

$3 x^{2}=18 \frac{3}{4}$

To find the value of x:

$3 x^{2}=18 \frac{3}{4}$

Convert mixed fraction into improper fraction.

$3 x^{2}= \frac{18\times 4+3}{4}$

$3 x^{2}= \frac{75}{4}$

Divide by 3 on both sides of the equation, we get

$x^{2}= \frac{25}{4}$

$x^{2}= \frac{5^2}{2^2}$

Taking square root on both side of the equation.

$\sqrt{ x^{2}}= \sqrt{\frac{5^2}{2^2}}$

$x=\pm \frac{5}{2}$

Convert improper fraction into mixed fraction.

$x=\pm 2\frac{1}{2}$

Hence option B is the correct answer.