Solve for h.

Question

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: \[ h \leq -2 \quad \text{or} \quad h \geq -1 \]