Option B:
[tex]$x=\pm 2\frac{1}{2}[/tex]
Solution:
Given expression:
[tex]$3 x^{2}=18 \frac{3}{4}[/tex]
To find the value of x:
[tex]$3 x^{2}=18 \frac{3}{4}[/tex]
Convert mixed fraction into improper fraction.
[tex]$3 x^{2}= \frac{18\times 4+3}{4}[/tex]
[tex]$3 x^{2}= \frac{75}{4}[/tex]
Divide by 3 on both sides of the equation, we get
[tex]$x^{2}= \frac{25}{4}[/tex]
[tex]$ x^{2}= \frac{5^2}{2^2}[/tex]
Taking square root on both side of the equation.
[tex]$\sqrt{ x^{2}}= \sqrt{\frac{5^2}{2^2}}[/tex]
[tex]$ x=\pm \frac{5}{2}[/tex]
Convert improper fraction into mixed fraction.
[tex]$x=\pm 2\frac{1}{2}[/tex]
Hence option B is the correct answer.
