Question

what is the solution to the equation?
$x + \frac{1}{3} = \frac{3}{5}$
$x = \frac{4}{15}$
$x = \frac{14}{15}$
(note: some options are partially unclear but the main equation and some options are as above)

Explanation:

Step1: Subtract $\frac{1}{3}$ from both sides

To solve for \( x \) in the equation \( x + \frac{1}{3} = \frac{3}{5} \), we subtract \( \frac{1}{3} \) from both sides of the equation. This gives us \( x = \frac{3}{5} - \frac{1}{3} \).

Step2: Find a common denominator and subtract

The common denominator of 5 and 3 is 15. We rewrite the fractions with the common denominator: \( \frac{3}{5} = \frac{9}{15} \) and \( \frac{1}{3} = \frac{5}{15} \). Now we subtract: \( x = \frac{9}{15} - \frac{5}{15} \).

Step3: Simplify the subtraction

Subtracting the numerators, we get \( x = \frac{9 - 5}{15} = \frac{4}{15} \).

Answer:

\( x = \frac{4}{15} \) (corresponding to the option \( x = \frac{4}{15} \))