Solve the following linear inequalities and write the solution in interval notation.

• A. $x<-\frac52$
• B. $x<-\frac{18}{5}$
• C. $x>-\frac{18}{5}$
• D. $x>-\frac52$

Answer: (C)

Verified step by step guidance

1. Start with the given inequality: \(-\frac{5}{6}x < 3\).
2. To isolate \(x\), divide both sides of the inequality by \(-\frac{5}{6}\). Remember, dividing by a negative number reverses the inequality sign.
3. Dividing by \(-\frac{5}{6}\) is the same as multiplying by its reciprocal \(-\frac{6}{5}\), so multiply both sides by \(-\frac{6}{5}\) and flip the inequality: \(x > 3 \times -\frac{6}{5}\).
4. Multiply the right side: \$3 \times -\frac{6}{5} = -\frac{18}{5}\(, so the inequality becomes \)x > -\frac{18}{5}$.
5. Write the solution in interval notation as \(\left(-\frac{18}{5}, \infty\right)\), which means all \(x\) values greater than \(-\frac{18}{5}\).