Solve for [tex]$x$[/tex]:
[tex]\[ \frac{3}{4} x + \frac{5}{4} = 4 x \][/tex]

A. [tex]$x = \frac{13}{5}$[/tex]
B. [tex]$x = \frac{5}{13}$[/tex]
C. [tex][tex]$x = \frac{3}{11}$[/tex][/tex]
D. [tex]$x = \frac{11}{3}$[/tex]



Answer :

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]