Question

now that you have the f terms on one side, and a constant number on the other side, you need to isolate f to solve for the value of f. what can you make to both sides of the equation to isolate f on the right side?
\\(\frac{2}{3}f + 5\\) = \\(f + 15\\)
\\(-\frac{2}{3}f\\) = \\(-\frac{2}{3}f\\)
5 = \\(\frac{1}{3}f + 15\\)
-15 = -15
-10 = \\(\frac{1}{3}f\\)
multiply both sides by f
multiply both sides by 3
subtract 10 from both sides

Explanation:

Step1: Subtract $\frac{2}{3}f$ from both sides

$\frac{2}{3}f + 5 - \frac{2}{3}f = f + 15 - \frac{2}{3}f$
$5 = \frac{1}{3}f + 15$

Step2: Subtract 15 from both sides

$5 - 15 = \frac{1}{3}f + 15 - 15$
$-10 = \frac{1}{3}f$

Step3: Multiply both sides by 3

$-10 \times 3 = \frac{1}{3}f \times 3$
$-30 = f$

Answer:

$f = -30$
The correct move to isolate $f$ on the right side (after combining $f$ terms) is to Subtract 10 from both sides is not needed; the correct next step after getting $-10 = \frac{1}{3}f$ is to multiply by 3, but the intermediate step to get constants on one side is subtracting 15 from both sides. The final isolated value of $f$ is $-30$.