Question

Solve for h.
h–7–5h≤–3 or –8h–3≥h+15
Write your answer as a compound inequality with integers.

Answer 1

To solve the inequalities \( h - 7 - 5h \leq -3 \) and \( -8h - 3 \geq h + 15 \), we will solve each inequality separately.

### Solving the first inequality:

1. Start with:
\[
h - 7 - 5h \leq -3
\]
2. Combine like terms:
\[
-4h - 7 \leq -3
\]
3. Add 7 to both sides:
\[
-4h \leq 4
\]
4. Divide by -4 (remember to reverse the inequality sign):
\[
h \geq -1
\]

### Solving the second inequality:

1. Start with:
\[
-8h - 3 \geq h + 15
\]
2. Add \( 8h \) to both sides:
\[
-3 \geq 9h + 15
\]
3. Subtract 15 from both sides:
\[
-18 \geq 9h
\]
4. Divide by 9:
\[
-2 \geq h \quad \text{or} \quad h \leq -2
\]

### Combining the results:

From the two inequalities, we have:
1. \( h \geq -1 \)
2. \( h \leq -2 \)

Since these two sets of results do not overlap, we write the solution in set notation as:
- \( h \geq -1 \) or \( h \leq -2 \)

### Final answer:

The final solution, expressed as a compound inequality, is:
\[
h \leq -2 \quad \text{or} \quad h \geq -1
\]