Solve the inequality for $$ y $$. $$ y+\frac{2}{5}\frac{1}{6} $$

Question

Solve the inequality for $$ y $$. $$ y+\frac{2}{5}>\frac{1}{6} $$

UpStudy AI · Accepted Answer

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 $$-\dfrac{7}{30}$$.

$$
y > -\frac{7}{30}
$$
$$ y > -\frac{7}{30} $$

Solve the inequality for \( y \). \[ y+\frac{2}{5}>\frac{1}{6} \]