Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( h = \frac{8}{5} \) or \( h = 1.6 \)
Solution
Certainly! Let's solve the equation step by step.
**Given Equation:**
\[
h - \frac{7}{8}h = \frac{1}{5}
\]
**Step 1: Combine Like Terms**
First, combine the terms on the left side of the equation. Both terms involve \( h \).
\[
h - \frac{7}{8}h = \left(1 - \frac{7}{8}\right)h
\]
\[
\left( \frac{8}{8} - \frac{7}{8} \right) h = \frac{1}{5}
\]
\[
\frac{1}{8}h = \frac{1}{5}
\]
**Step 2: Solve for \( h \)**
To isolate \( h \), multiply both sides of the equation by 8:
\[
h = 8 \times \frac{1}{5}
\]
\[
h = \frac{8}{5}
\]
\[
h = 1.6
\]
**Solution:**
\[
h = \frac{8}{5} \quad \text{or} \quad h = 1.6
\]
**Verification:**
Let's verify the solution by substituting \( h = \frac{8}{5} \) back into the original equation.
\[
h - \frac{7}{8}h = \frac{1}{5}
\]
\[
\frac{8}{5} - \frac{7}{8} \times \frac{8}{5} = \frac{1}{5}
\]
\[
\frac{8}{5} - \frac{56}{40} = \frac{1}{5}
\]
\[
\frac{8}{5} - \frac{7}{5} = \frac{1}{5}
\]
\[
\frac{1}{5} = \frac{1}{5} \quad \checkmark
\]
The solution \( h = \frac{8}{5} \) satisfies the original equation.
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Beyond the Answer
Let's solve the equation step by step! First, we can combine the terms on the left side: \( h - \frac{7}{8} h = \frac{1}{8} h \). So, we have: \( \frac{1}{8} h = \frac{1}{5} \). Now, to isolate \( h \), we multiply both sides by 8: \( h = 8 \times \frac{1}{5} = \frac{8}{5} \) or \( 1.6 \). And there you go! \( h = \frac{8}{5} \) or 1.6. Happy solving!
