The image contains three algebraic expressions where you are asked to multiply and simplify. Let’s go through each one step-by-step:

a) $\frac{3}{4} (8x + 2)$

Multiply $\frac{3}{4}$ by both terms inside the parentheses: $\frac{3}{4} \times 8x = 6x$ $\frac{3}{4} \times 2 = \frac{6}{4} = 1.5$ So, the simplified expression is: $6x + 1.5$

b) $\frac{2}{3} (6 - 9x)$

Multiply $\frac{2}{3}$ by both terms inside the parentheses: $\frac{2}{3} \times 6 = 4$ $\frac{2}{3} \times (-9x) = -6x$ So, the simplified expression is: $4 - 6x$

c) $\frac{5}{6} (12x - 18)$

Multiply $\frac{5}{6}$ by both terms inside the parentheses: $\frac{5}{6} \times 12x = 10x$ $\frac{5}{6} \times (-18) = -15$ So, the simplified expression is: $10x - 15$

Let me know if you'd like further explanation on any part or more details!

Here are 5 related questions for practice:

1. What happens if the parentheses in question (a) were $8x - 2$ instead of $8x + 2$?
2. How do you simplify expressions with more complicated fractions, such as $\frac{5}{8} (16x - 24)$?
3. How do you factor an expression like $6x + 1.5$?
4. What is the inverse operation of multiplying by a fraction?
5. Can these types of expressions be used in solving equations? How?

Tip: Always distribute the fraction to each term inside the parentheses separately, being mindful of signs!