To solve the inequality \(\frac{x}{2} + \frac{x}{3} \geq 176\), follow these steps:

1. **Find a common denominator** for the fractions on the left side:
   \[
   \text{The least common denominator (LCD) of 2 and 3 is 6}.
   \]
   So, rewrite each term with a denominator of 6:
   \[
   \frac{x}{2} = \frac{3x}{6}, \quad \frac{x}{3} = \frac{2x}{6}.
   \]

2. **Combine the fractions**:
   \[
   \frac{3x}{6} + \frac{2x}{6} = \frac{5x}{6}.
   \]
   The inequality becomes:
   \[
   \frac{5x}{6} \geq 176.
   \]

3. **Eliminate the denominator** by multiplying both sides of the inequality by 6:
   \[
   5x \geq 176 \times 6.
   \]
   Simplify the right side:
   \[
   5x \geq 1056.
   \]

4. **Solve for \(x\)** by dividing both sides by 5:
   \[
   x \geq \frac{1056}{5}.
   \]
   Simplify the division:
   \[
   x \geq 211.2.
   \]

Thus, the solution to the inequality is:
\[
x \geq 211.2.
\]

### Do you want details on any specific part of the process or have any questions?

Here are 5 related questions:
1. How do you find the least common denominator (LCD) of two fractions?
2. How do you combine fractions with different denominators?
3. What is the process for solving inequalities?
4. How do inequalities change when multiplying or dividing by a negative number?
5. How do you graph the solution to this inequality on a number line?

**Tip**: When solving inequalities, always check if multiplying or dividing by a negative number is necessary, as this reverses the inequality sign!

Learn how to solve the algebraic inequality (x/2) + (x/3) ≥ 176 with a step-by-step solution. This example involves combining fractions, finding a common denominator, and isolating the variable. Suitable for students in Grades 8-10.

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