Question

solve the following inequality for h. write your answer in simplest form.
-7h - 5(5h - 4) > -5h - 4 + h
answer
attempt 1 out of 2
h <
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Explanation:

Step1: Expand the left - hand side

We have the inequality \(-7h-5(5h - 4)>-5h-4 + h\). First, expand \(-5(5h - 4)\) using the distributive property \(a(b - c)=ab-ac\). Here, \(a=-5\), \(b = 5h\) and \(c = 4\), so \(-5(5h-4)=-25h + 20\). The inequality becomes \(-7h-25h + 20>-5h-4 + h\).

Step2: Combine like terms on both sides

On the left - hand side, combine \(-7h\) and \(-25h\): \(-7h-25h=-32h\), so the left - hand side is \(-32h + 20\). On the right - hand side, combine \(-5h\) and \(h\): \(-5h+h=-4h\), so the right - hand side is \(-4h-4\). Now the inequality is \(-32h + 20>-4h-4\).

Step3: Add \(32h\) to both sides

Adding \(32h\) to both sides of the inequality \(-32h + 20>-4h-4\) gives: \(-32h+32h + 20>-4h + 32h-4\), which simplifies to \(20>28h-4\).

Step4: Add 4 to both sides

Adding 4 to both sides of \(20>28h-4\) gives: \(20 + 4>28h-4 + 4\), so \(24>28h\).

Step5: Divide both sides by 28

Divide both sides of \(24>28h\) by 28. We get \(\frac{24}{28}>h\). Simplify \(\frac{24}{28}\) by dividing both the numerator and the denominator by 4: \(\frac{24\div4}{28\div4}=\frac{6}{7}\). So \(h<\frac{6}{7}\).

Answer:

\(h<\frac{6}{7}\)