Question

Solve the equation.
three fourths x minus one half
equalsone seventh
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Part 1
xequals
  
enter your response here
​(Type an integer or a simplified​ fraction.)

Answer 1

To solve the equation:

\[
\frac{3}{4} x - \frac{1}{2} = \frac{1}{7}
\]

first, we will isolate \( x \). Start by adding \(\frac{1}{2}\) to both sides:

\[
\frac{3}{4} x = \frac{1}{7} + \frac{1}{2}
\]

Now, we need to find a common denominator to add the fractions on the right side. The least common denominator of 7 and 2 is 14.

Convert \(\frac{1}{7}\) and \(\frac{1}{2}\) to have a denominator of 14:

\[
\frac{1}{7} = \frac{2}{14}
\]
\[
\frac{1}{2} = \frac{7}{14}
\]

Now add the fractions:

\[
\frac{1}{7} + \frac{1}{2} = \frac{2}{14} + \frac{7}{14} = \frac{9}{14}
\]

Now, substitute back into the equation:

\[
\frac{3}{4} x = \frac{9}{14}
\]

Next, multiply both sides by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\):

\[
x = \frac{9}{14} \cdot \frac{4}{3}
\]

Now perform the multiplication:

\[
x = \frac{9 \cdot 4}{14 \cdot 3} = \frac{36}{42}
\]

Now simplify \(\frac{36}{42}\):

\[
\frac{36}{42} = \frac{6}{7} \quad \text{(by dividing both numerator and denominator by 6)}
\]

Thus, the solution for \( x \) is:

\[
\boxed{\frac{6}{7}}
\]