Question
Solve the inequality for \( y \). \[ y+\frac{2}{5}>\frac{1}{6} \]
Ask by Little Zimmerman. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( y > -\frac{7}{30} \)
Solution
To solve the inequality for \( y \):
\[
y + \frac{2}{5} > \frac{1}{6}
\]
**Step 1: Isolate \( y \)**
Subtract \(\frac{2}{5}\) from both sides of the inequality to isolate \( y \):
\[
y > \frac{1}{6} - \frac{2}{5}
\]
**Step 2: Subtract the Fractions**
To subtract \(\frac{2}{5}\) from \(\frac{1}{6}\), find a common denominator. The least common denominator (LCD) of 6 and 5 is 30.
Convert each fraction to have the denominator of 30:
\[
\frac{1}{6} = \frac{5}{30} \quad \text{and} \quad \frac{2}{5} = \frac{12}{30}
\]
Now, subtract the fractions:
\[
\frac{5}{30} - \frac{12}{30} = \frac{5 - 12}{30} = \frac{-7}{30}
\]
**Step 3: Write the Final Inequality**
\[
y > -\frac{7}{30}
\]
**Solution:**
All real numbers \( y \) greater than \(-\dfrac{7}{30}\).
\[
y > -\frac{7}{30}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the inequality \( y + \frac{2}{5} > \frac{1}{6} \), start by isolating \( y \). Subtract \( \frac{2}{5} \) from both sides: \[ y > \frac{1}{6} - \frac{2}{5} \] Next, you need a common denominator to combine the fractions. The least common multiple of \( 6 \) and \( 5 \) is \( 30 \). Convert \( \frac{1}{6} \) and \( \frac{2}{5} \) to have the common denominator of \( 30 \): \[ \frac{1}{6} = \frac{5}{30}, \quad \frac{2}{5} = \frac{12}{30} \] Now substitute these back into the inequality: \[ y > \frac{5}{30} - \frac{12}{30} \] This simplifies to: \[ y > \frac{5 - 12}{30} = \frac{-7}{30} \] Thus, the solution to the inequality is: \[ y > -\frac{7}{30} \]
