Question

1. solve the inequality and graph its solution.

$r + 13 < 9$

Explanation:

Step1: Subtract 13 from both sides

To solve the inequality \( r + 13 < 9 \), we subtract 13 from both sides to isolate \( r \). Using the subtraction property of inequalities, we get \( r + 13 - 13 < 9 - 13 \).

Step2: Simplify both sides

Simplifying the left side, \( r + 13 - 13 = r \). Simplifying the right side, \( 9 - 13 = - 4 \). So the solution to the inequality is \( r < - 4 \).

For graphing the solution: On a number line, we draw an open circle at - 4 (because the inequality is strict, \( r < - 4 \), not \( r\leq - 4 \)) and shade the region to the left of - 4 to represent all values of \( r \) that are less than - 4.

Answer:

The solution to the inequality is \( r < - 4 \). The graph has an open circle at - 4 and shading to the left of - 4 on the number line.