Question

-3x - p > 0
in the inequality, p represents any real number.
solve the inequality for x.
○ x < -3/p
○ x > p/-3
○ x < p/-3
○ x < p + 3
○ x < p/3

Explanation:

Step1: Add \( p \) to both sides

To isolate the term with \( z \), we add \( p \) to both sides of the inequality \( -3z - p > 0 \). This gives us \( -3z - p + p > 0 + p \), which simplifies to \( -3z > p \).

Step2: Divide both sides by -3 (and reverse inequality)

When dividing an inequality by a negative number, the direction of the inequality sign must be reversed. So we divide both sides of \( -3z > p \) by \( -3 \). This gives \( \frac{-3z}{-3} < \frac{p}{-3} \), which simplifies to \( z < \frac{p}{-3} \) (or \( z < -\frac{p}{3} \), but in the form matching the options, it's \( z < \frac{p}{-3} \)).

Answer:

\( z < \frac{p}{-3} \) (corresponding to the option \( z < \frac{p}{-3} \))