Question

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Part 1
Solve the equation.
three fourths x minus one eighth
equalsone third

Answer 1

To solve the equation \(\frac{3}{4}x - \frac{1}{8} = \frac{1}{3}\), we can follow these steps:

1. Start by isolating the term with \(x\):
\[
\frac{3}{4}x = \frac{1}{3} + \frac{1}{8}
\]

2. To add the fractions on the right side, we need a common denominator. The least common multiple of 3 and 8 is 24.
Rewrite \(\frac{1}{3}\) and \(\frac{1}{8}\) with a denominator of 24:
\[
\frac{1}{3} = \frac{8}{24}, \quad \frac{1}{8} = \frac{3}{24}
\]

3. Now add the two fractions:
\[
\frac{1}{3} + \frac{1}{8} = \frac{8}{24} + \frac{3}{24} = \frac{11}{24}
\]

4. Now, substitute back into the equation:
\[
\frac{3}{4}x = \frac{11}{24}
\]

5. To solve for \(x\), multiply both sides by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\):
\[
x = \frac{11}{24} \cdot \frac{4}{3}
\]

6. Multiply the fractions:
\[
x = \frac{11 \cdot 4}{24 \cdot 3} = \frac{44}{72}
\]

7. Simplify \(\frac{44}{72}\) by finding the greatest common divisor (GCD), which is 4:
\[
x = \frac{44 \div 4}{72 \div 4} = \frac{11}{18}
\]

So the solution to the equation is:
\[
\boxed{\frac{11}{18}}
\]