Question

solve each inequality. graph and check the solution. (ex

1. ( 5d - 13 < 32 ) _____________

3.

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

Explanation:

Step1: Add 13 to both sides

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

Step2: Divide both sides by 5

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

Answer:

The solution to the inequality \( 5d - 13 < 32 \) is \( d < 9 \). To graph this, we draw an open circle at 9 on the number line (since \( d \) is not equal to 9) and shade the region to the left of 9. To check, we can pick a value less than 9, say \( d = 8 \). Substituting into the original inequality: \( 5(8) - 13 = 40 - 13 = 27 \), and \( 27 < 32 \) is true. If we pick a value greater than or equal to 9, say \( d = 9 \), we get \( 5(9) - 13 = 45 - 13 = 32 \), and \( 32 < 32 \) is false, which confirms our solution.