Question

solve each of the following inequalities.

1. ( 25 - 2y > 3 )
2. ( 2(5 + 2n) geq 12 )

Explanation:

Problem 15: Solve \( 25 - 2y > 3 \)

Step 1: Subtract 25 from both sides

To isolate the term with \( y \), we subtract 25 from both sides of the inequality.
\( 25 - 2y - 25 > 3 - 25 \)
Simplifying both sides, we get:
\( -2y > -22 \)

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

When dividing an inequality by a negative number, the direction of the inequality sign must be reversed.
\( \frac{-2y}{-2} < \frac{-22}{-2} \)
Simplifying both sides, we get:
\( y < 11 \)

Step 1: Divide both sides by 2

To simplify the left - hand side, we divide both sides of the inequality by 2.
\( \frac{2(5 + 2n)}{2} \geq \frac{12}{2} \)
Simplifying both sides, we get:
\( 5 + 2n \geq 6 \)

Step 2: Subtract 5 from both sides

To isolate the term with \( n \), we subtract 5 from both sides.
\( 5 + 2n - 5 \geq 6 - 5 \)
Simplifying both sides, we get:
\( 2n \geq 1 \)

Step 3: Divide both sides by 2

To solve for \( n \), we divide both sides by 2.
\( \frac{2n}{2} \geq \frac{1}{2} \)
Simplifying both sides, we get:
\( n \geq \frac{1}{2} \)

Answer:

\( y < 11 \)

Problem 16: Solve \( 2(5 + 2n) \geq 12 \)