Question

question
solve the following inequality for h. write your answer in simplest form.
8 + 5(-9h - 2) > -10h - 6 - 1
answer attempt 1 out of 5
h <
submit answer

Explanation:

Step1: Simplify left side

First, distribute the 5 on the left side: \(8 + 5(-9h - 2)=8 - 45h - 10\). Then combine like terms: \(8 - 10 - 45h=-2 - 45h\).

Step2: Simplify right side

Combine the constants on the right side: \(-10h - 6 - 1=-10h - 7\).

Step3: Rewrite the inequality

Now the inequality is \(-2 - 45h > -10h - 7\).

Step4: Add \(45h\) to both sides

Adding \(45h\) to both sides gives \(-2 > 35h - 7\).

Step5: Add 7 to both sides

Adding 7 to both sides: \(5 > 35h\).

Step6: Divide by 35

Divide both sides by 35: \(\frac{5}{35}>h\), which simplifies to \(\frac{1}{7}>h\) or \(h < \frac{1}{7}\).

Answer:

\(\frac{1}{7}\)