Question

solve the equation. what is the value of f?
one way you can start solving is to make sure there are only f terms on one side. what move can you make to both sides of the equation to get rid of the \\(\frac{2}{3}f\\) on the left, while keeping the equation balanced?
\\(\frac{2}{3}f + 5 = f + 15\\)
add \\(\frac{2}{3}f\\) to both sides
divide both sides by \\(\frac{2}{3}f\\)
subtract \\(\frac{2}{3}f\\) from both sides
multiply both sides by \\(\frac{2}{3}f\\)

Explanation:

Step1: Choose correct balancing step

To eliminate $\frac{2}{3}f$ from the left side while keeping the equation balanced, we subtract $\frac{2}{3}f$ from both sides.
$\frac{2}{3}f + 5 - \frac{2}{3}f = f + 15 - \frac{2}{3}f$

Step2: Simplify both sides

Simplify the left side to isolate the constant, and combine like terms on the right.
$5 = \frac{1}{3}f + 15$

Step3: Isolate the f-term

Subtract 15 from both sides to move the constant to the left.
$5 - 15 = \frac{1}{3}f$
$-10 = \frac{1}{3}f$

Step4: Solve for f

Multiply both sides by 3 to solve for f.
$f = -10 \times 3$

Answer:

Correct balancing move: Subtract $\frac{2}{3}f$ from both sides
Value of $f$: $-30$