3 - 4(y + 2) is less than or equal to 6 + 4(2y + 1)

Answer 1

To solve the inequality \( 3 - 4(y + 2) \leq 6 + 4(2y + 1) \), follow these steps:

1. Distribute on both sides: \[ 3 - 4y - 8 \leq 6 + 8y + 4 \] This simplifies to: \[ -4y - 5 \leq 10 + 8y \]

2. Rearrange the inequality to bring all \( y \) terms to one side and the constant terms to the other side: \[ -4y - 8y \leq 10 + 5 \] Simplifying that gives: \[ -12y \leq 15 \]

3. Divide both sides by -12. Remember that when you divide by a negative number, the inequality sign flips: \[ y \geq -\frac{15}{12} \]

4. Simplify the fraction: \[ y \geq -\frac{5}{4} \]

So, the solution to the inequality is: \[ y \geq -\frac{5}{4} \]