Answer :
To solve the equation [tex]\(\frac{4}{5}x + \frac{1}{3} = 2\)[/tex], follow these steps:
1. Isolate the [tex]\(x\)[/tex]-term:
First, we need to get rid of the constant term [tex]\(\frac{1}{3}\)[/tex] on the left side of the equation.
[tex]\[
\frac{4}{5}x + \frac{1}{3} = 2
\][/tex]
Subtract [tex]\(\frac{1}{3}\)[/tex] from both sides:
[tex]\[
\frac{4}{5}x = 2 - \frac{1}{3}
\][/tex]
2. Simplify the right side of the equation:
We need a common denominator to subtract these fractions. The common denominator of 2 and [tex]\(\frac{1}{3}\)[/tex] is 3:
[tex]\[
2 = \frac{6}{3}
\][/tex]
So,
[tex]\[
2 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3}
\][/tex]
Now the equation is:
[tex]\[
\frac{4}{5}x = \frac{5}{3}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to multiply both sides by the reciprocal of [tex]\(\frac{4}{5}\)[/tex] which is [tex]\(\frac{5}{4}\)[/tex]:
[tex]\[
x = \frac{5}{4} \times \frac{5}{3}
\][/tex]
Multiply the fractions:
[tex]\[
x = \frac{5 \times 5}{4 \times 3} = \frac{25}{12}
\][/tex]
So the solution to the equation [tex]\(\frac{4}{5}x + \frac{1}{3} = 2\)[/tex] is:
[tex]\[
x = \frac{25}{12}
\][/tex]
Therefore, the correct answer is:
C [tex]\( \quad x = \frac{25}{12} \)[/tex]
1. Isolate the [tex]\(x\)[/tex]-term:
First, we need to get rid of the constant term [tex]\(\frac{1}{3}\)[/tex] on the left side of the equation.
[tex]\[
\frac{4}{5}x + \frac{1}{3} = 2
\][/tex]
Subtract [tex]\(\frac{1}{3}\)[/tex] from both sides:
[tex]\[
\frac{4}{5}x = 2 - \frac{1}{3}
\][/tex]
2. Simplify the right side of the equation:
We need a common denominator to subtract these fractions. The common denominator of 2 and [tex]\(\frac{1}{3}\)[/tex] is 3:
[tex]\[
2 = \frac{6}{3}
\][/tex]
So,
[tex]\[
2 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3}
\][/tex]
Now the equation is:
[tex]\[
\frac{4}{5}x = \frac{5}{3}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to multiply both sides by the reciprocal of [tex]\(\frac{4}{5}\)[/tex] which is [tex]\(\frac{5}{4}\)[/tex]:
[tex]\[
x = \frac{5}{4} \times \frac{5}{3}
\][/tex]
Multiply the fractions:
[tex]\[
x = \frac{5 \times 5}{4 \times 3} = \frac{25}{12}
\][/tex]
So the solution to the equation [tex]\(\frac{4}{5}x + \frac{1}{3} = 2\)[/tex] is:
[tex]\[
x = \frac{25}{12}
\][/tex]
Therefore, the correct answer is:
C [tex]\( \quad x = \frac{25}{12} \)[/tex]