Sure, let's solve the equation step by step to find the value of [tex]\( x \)[/tex]:
Given equation:
[tex]\[
\frac{3}{4} x + \frac{5}{4} = 4 x
\][/tex]
1. Isolate the [tex]\( x \)[/tex]-terms on one side:
First, move [tex]\(\frac{3}{4} x\)[/tex] to the right side of the equation by subtracting [tex]\(\frac{3}{4} x\)[/tex] from both sides:
[tex]\[
\frac{5}{4} = 4 x - \frac{3}{4} x
\][/tex]
2. Combine like terms:
Combine the [tex]\( x \)[/tex]-terms on the right side:
[tex]\[
4 x - \frac{3}{4} x = \left(4 - \frac{3}{4}\right) x
\][/tex]
To combine these, find a common denominator (which is 4) for the fraction:
[tex]\[
4 = \frac{16}{4}
\][/tex]
Thus,
[tex]\[
4 x - \frac{3}{4} x = \frac{16}{4} x - \frac{3}{4} x = \frac{13}{4} x
\][/tex]
So the equation now is:
[tex]\[
\frac{5}{4} = \frac{13}{4} x
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], divide both sides of the equation by [tex]\(\frac{13}{4}\)[/tex]:
[tex]\[
x = \frac{\frac{5}{4}}{\frac{13}{4}} = \frac{5}{4} \times \frac{4}{13} = \frac{5}{13}
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{3}{4} x + \frac{5}{4} = 4 x\)[/tex] is:
[tex]\[
x = \frac{5}{13}
\][/tex]
This matches one of the given multiple-choice answers. Thus, the correct answer is:
[tex]\[
\boxed{x = \frac{5}{13}}
\][/tex]
