Question

solve each inequality. graph and check the solution. (example 2)

1. ( 5d - 13 < 32 )

(number line: 0,2,4,6,8,10,12,14,16,18,20)

1. ( -4b + 9 leq -7 )

(number line: 0,2,4,6,8,10,12,14,16,18,20)
circle any given values that make the inequality true. (example 3)

Explanation:

Problem 2: Solve \( 5d - 13 < 32 \)

Step 1: Add 13 to both sides

To isolate the term with \( d \), we add 13 to both sides of the inequality.
\( 5d - 13 + 13 < 32 + 13 \)
Simplifying both sides, we get:
\( 5d < 45 \)

Step 2: Divide both sides by 5

To solve for \( d \), we divide both sides of the inequality by 5.
\( \frac{5d}{5} < \frac{45}{5} \)
Simplifying both sides, we get:
\( d < 9 \)

Step 1: Subtract 9 from both sides

To isolate the term with \( b \), we subtract 9 from both sides of the inequality.
\( -4b + 9 - 9 \leq -7 - 9 \)
Simplifying both sides, we get:
\( -4b \leq -16 \)

Step 2: Divide both sides by -4 (and reverse the inequality)

When dividing an inequality by a negative number, we reverse the inequality sign.
\( \frac{-4b}{-4} \geq \frac{-16}{-4} \)
Simplifying both sides, we get:
\( b \geq 4 \)

Answer:

\( d < 9 \)

Problem 3: Solve \( -4b + 9 \leq -7 \)