Question

solve the following inequality for f. write your answer in simplest form. -f - 3 < 2f - 7

Explanation:

Step1: Add \( f \) to both sides

To get rid of the \( -f \) on the left, we add \( f \) to both sides of the inequality. This gives us:
\( -f - 3 + f < 2f - 7 + f \)
Simplifying both sides, the \( -f \) and \( +f \) on the left cancel out, and on the right we combine like terms:
\( -3 < 3f - 7 \)

Step2: Add 7 to both sides

Now we want to isolate the term with \( f \), so we add 7 to both sides:
\( -3 + 7 < 3f - 7 + 7 \)
Simplifying both sides, we get:
\( 4 < 3f \)

Step3: Divide both sides by 3

To solve for \( f \), we divide both sides of the inequality by 3:
\( \frac{4}{3} < f \)
Which can also be written as \( f > \frac{4}{3} \)

Answer:

\( f > \frac{4}{3} \)