Question

3 - 2y ≤ -25; -4c + 8 ≤ 10; -\frac{1}{3}x + 5 > 9

Explanation:

Solving \( 3 - 2y \leq -25 \)

Step1: Subtract 3 from both sides

To isolate the term with \( y \), we subtract 3 from both sides of the inequality.
\( 3 - 2y - 3 \leq -25 - 3 \)
Simplifying both sides, we get:
\( -2y \leq -28 \)

Step2: Divide by -2 (and reverse inequality)

When dividing an inequality by a negative number, we must reverse the inequality sign. We divide both sides by -2.
\( \frac{-2y}{-2} \geq \frac{-28}{-2} \)
Simplifying, we find:
\( y \geq 14 \)

Solving \( -4c + 8 \leq 10 \)

Step1: Subtract 8 from both sides

To isolate the term with \( c \), we subtract 8 from both sides of the inequality.
\( -4c + 8 - 8 \leq 10 - 8 \)
Simplifying both sides, we get:
\( -4c \leq 2 \)

Step2: Divide by -4 (and reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. We divide both sides by -4.
\( \frac{-4c}{-4} \geq \frac{2}{-4} \)
Simplifying, we find:
\( c \geq -\frac{1}{2} \)

Solving \( -\frac{1}{3}x + 5 > 9 \)

Step1: Subtract 5 from both sides

To isolate the term with \( x \), we subtract 5 from both sides of the inequality.
\( -\frac{1}{3}x + 5 - 5 > 9 - 5 \)
Simplifying both sides, we get:
\( -\frac{1}{3}x > 4 \)

Step2: Multiply by -3 (and reverse inequality)

When multiplying an inequality by a negative number, we reverse the inequality sign. We multiply both sides by -3.
\( -\frac{1}{3}x \times (-3) < 4 \times (-3) \)
Simplifying, we find:
\( x < -12 \)

Answer:

s:

• For \( 3 - 2y \leq -25 \): \( \boldsymbol{y \geq 14} \)
• For \( -4c + 8 \leq 10 \): \( \boldsymbol{c \geq -\frac{1}{2}} \)
• For \( -\frac{1}{3}x + 5 > 9 \): \( \boldsymbol{x < -12} \)