Solve the inequality for $$ y $$. $$ y-38 \geq-5(2-3 y) $$ Simplify your answer as much as possible. $$ \square $$

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UpStudy AI · Accepted Answer

1. Start with the inequality:
   $$
   y - 38 \geq -5(2 - 3y)
   $$

2. Distribute on the right-hand side:
   $$
   -5(2 - 3y) = -10 + 15y
   $$
   So the inequality becomes:
   $$
   y - 38 \geq -10 + 15y
   $$

3. Subtract $$ y $$ from both sides to collect like terms:
   $$
   y - 38 - y \geq -10 + 15y - y
   $$
   Simplifying:
   $$
   -38 \geq -10 + 14y
   $$

4. Add $$ 10 $$ to both sides:
   $$
   -38 + 10 \geq -10 + 10 + 14y
   $$
   Which simplifies to:
   $$
   -28 \geq 14y
   $$

5. Divide both sides by $$ 14 $$:
   $$
   \frac{-28}{14} \geq y
   $$
   Simplifying the fraction:
   $$
   -2 \geq y
   $$
   Alternatively, rewriting the inequality:
   $$
   y \leq -2
   $$

$$\boxed{y \leq -2}$$
$$ y \leq -2 $$

Solve the inequality for .

Simplify your answer as much as possible.

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Solve the inequality for . Simplify your answer as much as possible.