Solve  2x-4/6 ≥ -5x+2
  Write the solution using set-builder notation.

Let's solve the inequality:

\[
\frac{2x - 4}{6} \geq -5x + 2
\]

### Step 1: Clear the fraction
Multiply both sides of the inequality by 6 to eliminate the denominator:

\[
2x - 4 \geq 6(-5x + 2)
\]

Distribute the 6 on the right-hand side:

\[
2x - 4 \geq -30x + 12
\]

### Step 2: Combine like terms
Move all terms involving \(x\) to one side and constants to the other:

\[
2x + 30x \geq 12 + 4
\]

Simplify:

\[
32x \geq 16
\]

### Step 3: Solve for \(x\)
Divide both sides by 32:

\[
x \geq \frac{16}{32}
\]

Simplify:

\[
x \geq \frac{1}{2}
\]

### Final Answer: Set-builder notation
The solution in set-builder notation is:

\[
\{ x \mid x \geq \frac{1}{2} \}
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you solve inequalities with multiple fractions?
2. What changes if the inequality sign flips?
3. How do you graph the solution of an inequality?
4. Can you apply the same method for a quadratic inequality?
5. What happens when you multiply or divide by a negative number in an inequality?

**Tip:** Always flip the inequality sign when multiplying or dividing by a negative number.

Solve 2x - 4/6 ≥ -5x + 2. Write the solution using set-builder notation.

Learn how to solve the linear inequality 2x - 4/6 ≥ -5x + 2 using set-builder notation. This step-by-step guide includes clearing fractions, combining like terms, and applying properties of inequalities. Suitable for students in Grades 7-9.

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