Question

1< y+10/3 ≤5
Write your answer as a compound inequality with integers.

Answer 1

To solve the inequality \( 1 < \frac{y + 10}{3} \leq 5 \), we'll break it into two parts and solve each part separately.

### Step 1: Solve the left part of the inequality
1. Start with the left side:
\[
1 < \frac{y + 10}{3}
\]
2. Multiply both sides by 3:
\[
3 < y + 10
\]
3. Subtract 10 from both sides:
\[
3 - 10 < y
\]
\[
-7 < y \quad \text{or} \quad y > -7
\]

### Step 2: Solve the right part of the inequality
1. Now, solve the right side:
\[
\frac{y + 10}{3} \leq 5
\]
2. Multiply both sides by 3:
\[
y + 10 \leq 15
\]
3. Subtract 10 from both sides:
\[
y \leq 15 - 10
\]
\[
y \leq 5
\]

### Step 3: Combine the results
Now, we can combine the two results:
\[
-7 < y \leq 5
\]

### Step 4: Write the answer in compound inequality notation
In compound inequality notation, the answer is:
\[
-7 < y \leq 5
\]

As integers, the solution can be expressed as:
\[
y \in (-7, 5]
\]

**Final Answer:**
\((-7, 5]\) (or in interval notation: all integers \(y\) such that \(y > -7\) and \(y \leq 5\))