College

What is the solution to [tex]\frac{4}{5} x + \frac{1}{3} = 2[/tex]?

A. [tex]x = \frac{12}{25}[/tex]

B. [tex]x = 25[/tex]

C. [tex]x = \frac{25}{12}[/tex]

D. [tex]x = 13[/tex]

Answer :

To solve the equation [tex]\(\frac{4}{5}x + \frac{1}{3} = 2\)[/tex], we need to isolate [tex]\(x\)[/tex] by following these steps:

1. Eliminate the fraction on the right side:
Start by getting rid of the constant term on the left side. Subtract [tex]\(\frac{1}{3}\)[/tex] from both sides of the equation:
[tex]\[
\frac{4}{5}x = 2 - \frac{1}{3}
\][/tex]

2. Simplify the right side:
To subtract these numbers, first convert 2 into a fraction with a denominator of 3:
[tex]\[
2 = \frac{6}{3}
\][/tex]
Now, perform the subtraction:
[tex]\[
\frac{6}{3} - \frac{1}{3} = \frac{5}{3}
\][/tex]
Now the equation becomes:
[tex]\[
\frac{4}{5}x = \frac{5}{3}
\][/tex]

3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], multiply both sides by the reciprocal of [tex]\(\frac{4}{5}\)[/tex], which is [tex]\(\frac{5}{4}\)[/tex]:
[tex]\[
x = \frac{5}{3} \times \frac{5}{4}
\][/tex]

4. Multiply the fractions:
Multiply the numerators and the denominators:
[tex]\[
x = \frac{5 \times 5}{3 \times 4} = \frac{25}{12}
\][/tex]

Thus, the solution is:
[tex]\[
x = \frac{25}{12}
\][/tex]

So, the correct answer is C: [tex]\(x=\frac{25}{12}\)[/tex].