The image contains an inequality problem with two parts:

1. $-6(y - 3) \leq 36$
2. $12 + y < 15$

We need to solve these inequalities and express the solution in interval notation.

Step 1: Solve the first inequality:

$-6(y - 3) \leq 36$ Distribute the $-6$: $-6y + 18 \leq 36$ Subtract 18 from both sides: $-6y \leq 18$ Divide by $-6$ (and reverse the inequality because of dividing by a negative number): $y \geq -3$

Step 2: Solve the second inequality:

$12 + y < 15$ Subtract 12 from both sides: $y < 3$

Step 3: Combine the solutions:

The first inequality gives $y \geq -3$ and the second gives $y < 3$.

In interval notation, this is: $[-3, 3)$

This is the final solution for the combined inequalities.

Would you like more details or have any other questions?

Related Questions:

1. How do you solve inequalities with multiplication or division involving negatives?
2. Can you graph the solution to these inequalities on a number line?
3. How does reversing the inequality sign work?
4. What are the differences between "and" & "or" conditions in inequalities?
5. How can interval notation be used for compound inequalities?

Tip:

Always remember to flip the inequality sign when multiplying or dividing by a negative number!