Question

write an inequality with x isolated on the left side that is equivalent to the given inequali dx + ey > f. assume d > 0.

Explanation:

Step1: Subtract \( Ey \) from both sides

To isolate the term with \( x \), we perform the subtraction operation. The original inequality is \( Dx + Ey > F \). Subtracting \( Ey \) from both sides gives \( Dx + Ey - Ey > F - Ey \), which simplifies to \( Dx > F - Ey \).

Step2: Divide both sides by \( D \) (since \( D > 0 \), the inequality sign remains the same)

We divide each side of the inequality \( Dx > F - Ey \) by \( D \). Using the division property of inequalities (for positive divisors, the inequality sign doesn't change), we get \( \frac{Dx}{D} > \frac{F - Ey}{D} \), which simplifies to \( x > \frac{F - Ey}{D} \).

Answer:

\( x > \frac{F - Ey}{D} \)