Question

Negative 2 is less than or equal to 2x + 1/3

Answer 1

To solve the inequality \(-2 \leq 2x + \frac{1}{3}\), follow these steps:

1. **Isolate the term involving \(x\)**:
Subtract \(\frac{1}{3}\) from both sides:

\[
-2 - \frac{1}{3} \leq 2x
\]

2. **Simplify the left side**:
First, convert \(-2\) to a fraction that has a denominator of 3:

\[
-2 = -\frac{6}{3}
\]

Now, combine the fractions:

\[
-\frac{6}{3} - \frac{1}{3} = -\frac{7}{3}
\]

So the inequality is now:

\[
-\frac{7}{3} \leq 2x
\]

3. **Divide by 2**:
Divide both sides of the inequality by 2 to solve for \(x\):

\[
-\frac{7}{3} \div 2 \leq x \quad \text{or} \quad x \geq -\frac{7}{3} \cdot \frac{1}{2}
\]

This simplifies to:

\[
x \geq -\frac{7}{6}
\]

So the solution to the inequality is:

\[
x \geq -\frac{7}{6}
\]