https://file.aiquickdraw.com/mathbot/file/172679788850367gj091c.jpg

The inequality you provided from the image is:

\[
\frac{3}{8}x - 4 \leq \frac{3}{4}x + 2
\]

### To solve this inequality:

1. **Eliminate the fractions** by multiplying every term by the least common denominator (LCD). The LCD of 8 and 4 is 8.

\[
8 \left(\frac{3}{8}x - 4\right) \leq 8 \left(\frac{3}{4}x + 2\right)
\]

This simplifies to:

\[
3x - 32 \leq 6x + 16
\]

2. **Isolate the variable terms** on one side. Subtract \(3x\) from both sides:

\[
-32 \leq 3x + 16
\]

3. **Move the constant terms** to the other side by subtracting 16 from both sides:

\[
-48 \leq 3x
\]

4. **Solve for \(x\)** by dividing both sides by 3:

\[
x \geq -16
\]

### Final solution:
\[
x \geq -16
\]

This means \(x\) must be greater than or equal to \(-16\).

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Would you like more details, or do you have any further questions?

Here are some related questions you might find helpful:
1. How do you handle inequalities involving negative numbers?
2. What are the differences between solving equalities and inequalities?
3. How do you represent inequalities on a number line?
4. How does multiplying or dividing by a negative number affect an inequality?
5. Can inequalities have more than one solution?

**Tip:** Always remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.

Solve the inequality: (3/8)x - 4 ≤ (3/4)x + 2

Learn how to solve the inequality (3/8)x - 4 ≤ (3/4)x + 2 by eliminating fractions and isolating the variable. This step-by-step guide explores key algebraic concepts and suitable techniques for Grades 8-10.

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