https://file.aiquickdraw.com/mathbot/file/17271940600414uvrxeqs.jpg

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!

Solve the inequality problem: -6(y - 3) ≤ 36 or 12 + y < 15. Express your answer in interval notation.

Learn how to solve the linear inequality problem: -6(y - 3) ≤ 36 or 12 + y < 15. This solution covers key algebraic concepts like solving inequalities and understanding interval notation. Suitable for students in Grades 8-10.

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