Question
Solve for \( x \) \[ x-\frac{5}{6}=-\frac{1}{5} \] Simnlify vour
Ask by Bob Pierce. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = \frac{19}{30} \)
Solution
To solve for \( x \) in the equation:
\[
x - \frac{5}{6} = -\frac{1}{5}
\]
**Step 1:** **Isolate \( x \)**
Add \(\frac{5}{6}\) to both sides of the equation to isolate \( x \):
\[
x = -\frac{1}{5} + \frac{5}{6}
\]
**Step 2:** **Find a Common Denominator**
To add the fractions, find a common denominator. The least common denominator (LCD) of 5 and 6 is 30.
\[
-\frac{1}{5} = -\frac{6}{30} \quad \text{and} \quad \frac{5}{6} = \frac{25}{30}
\]
**Step 3:** **Add the Fractions**
\[
x = -\frac{6}{30} + \frac{25}{30} = \frac{19}{30}
\]
**Final Answer:**
\[
x = \frac{19}{30}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve for \( x \), start by adding \(\frac{5}{6}\) to both sides of the equation: \[ x = -\frac{1}{5} + \frac{5}{6} \] Next, to combine the fractions, find a common denominator, which is 30 in this case: \[ -\frac{1}{5} = -\frac{6}{30} \quad \text{and} \quad \frac{5}{6} = \frac{25}{30} \] Now substitute these values back into the equation: \[ x = -\frac{6}{30} + \frac{25}{30} = \frac{25 - 6}{30} = \frac{19}{30} \] So, the solution is: \[ x = \frac{19}{30} \]
