Question

If \(-3x + 17<-13\), then

• A. \(x \in (10,\ \infty)\)
• B. \(x \in [10,\ \infty)\)
• C. \(x \in (-\infty,\ 10)\)
• D. \(x \in [-10,\ 10)\)

Hint:

Whenever you divide or multiply an inequality by a negative number, always textbfreverse the inequality sign.

Answer 1

The Correct Option is A

Step 1: Start with the given inequality. \[ -3x + 17<-13 \] Step 2: Transpose the constant term. \[ -3x<-13 - 17 \] \[ -3x<-30 \] Step 3: Divide both sides by \(-3\). (Note: Dividing by a negative number reverses the inequality sign.) \[ x>10 \] Step 4: Write the solution in interval notation. \[ x \in (10,\ \infty) \] Step 5: Final conclusion. The correct option is \(\boxed{(A)}\).