Question

graph the solution of this inequality: $-2x + 13 < 9$

Explanation:

Step1: Subtract 13 from both sides

To isolate the term with \( x \), we subtract 13 from both sides of the inequality \( -2x + 13 < 9 \). This gives us \( -2x + 13 - 13 < 9 - 13 \), which simplifies to \( -2x < -4 \).

Step2: Divide by -2 (and reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. Dividing both sides of \( -2x < -4 \) by -2, we get \( \frac{-2x}{-2} > \frac{-4}{-2} \), which simplifies to \( x > 2 \).

Answer:

The correct solution to the inequality \( -2x + 13 < 9 \) is \( x > 2 \). To graph this, we would have an open circle at 2 (since the inequality is strict, \( x > 2 \) not \( x \geq 2 \)) and a line extending to the right from 2 on the number line.