Question

write an inequality with x isolated on the left side that is equivalent to the given inequality. ax - by > c, assume a < 0

Explanation:

Step1: Add \( By \) to both sides

To isolate the term with \( x \), we add \( By \) to both sides of the inequality \( Ax - By > C \). This gives us \( Ax - By + By > C + By \), which simplifies to \( Ax > C + By \).

Step2: Divide both sides by \( A \) (note \( A < 0 \))

Since \( A < 0 \), when we divide both sides of an inequality by a negative number, the direction of the inequality sign changes. So we divide each side of \( Ax > C + By \) by \( A \). This gives \( x < \frac{C + By}{A} \) (because dividing by a negative \( A \) reverses the \( > \) to \( < \)).

Answer:

\( x < \frac{C + By}{A} \)