Let's simplify the expression:

\[
\frac{3}{4}(3x + 6) - \frac{1}{4}(5x - 24)
\]

### Step 1: Distribute the fractions to the terms inside the parentheses.

\[
\frac{3}{4}(3x) + \frac{3}{4}(6) - \frac{1}{4}(5x) + \frac{1}{4}(24)
\]

This gives:

\[
\frac{9x}{4} + \frac{18}{4} - \frac{5x}{4} + \frac{24}{4}
\]

### Step 2: Combine like terms.

First, simplify the constants:

\[
\frac{18}{4} + \frac{24}{4} = \frac{42}{4} = \frac{21}{2}
\]

Now combine the \( x \)-terms:

\[
\frac{9x}{4} - \frac{5x}{4} = \frac{4x}{4} = x
\]

### Final simplified expression:

\[
x + \frac{21}{2}
\]

The expression in its simplest form is:

\[
x + \frac{21}{2}
\]

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:
1. How do you solve linear equations involving fractions?
2. What is the difference between distributing a fraction and multiplying?
3. How would this expression change if you had different coefficients?
4. Can you convert mixed numbers back to improper fractions?
5. How do you factor polynomials with fractional coefficients?

**Tip:** Always distribute fractions carefully, and watch for opportunities to combine like terms!

3/4(3x + 6) - 1/4(5x - 24) in simplest terms

Learn how to simplify the algebraic expression 3/4(3x + 6) - 1/4(5x - 24) step by step. This problem involves using the distributive property, combining like terms, and working with fractions. Suitable for students in Grades 7-9.

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