Question

1. $-\frac{1}{2}(y - x)$

$-1.5(-3 + 4n + 8.2)$

Explanation:

First Expression: $-\frac{1}{2}(y - x)$

Step1: Apply distributive property

Multiply $-\frac{1}{2}$ with each term inside the parentheses.
$-\frac{1}{2} \times y + (-\frac{1}{2}) \times (-x)$

Step2: Simplify each term

Simplify the two terms: $-\frac{1}{2}y + \frac{1}{2}x$ or rearranged as $\frac{1}{2}x - \frac{1}{2}y$

Second Expression: $-1.5(-3 + 4n + 8.2)$

Step1: Combine like terms inside parentheses

First, combine the constant terms: $-3 + 8.2 = 5.2$
So the expression becomes $-1.5(5.2 + 4n)$

Step2: Apply distributive property

Multiply $-1.5$ with each term inside the parentheses.
$-1.5 \times 5.2 + (-1.5) \times 4n$

Step3: Calculate each product

Calculate $-1.5 \times 5.2 = -7.8$ and $-1.5 \times 4n = -6n$
So the simplified expression is $-7.8 - 6n$

Answer:

s:

1. For $-\frac{1}{2}(y - x)$: $\boldsymbol{\frac{1}{2}x - \frac{1}{2}y}$ (or $-\frac{1}{2}y + \frac{1}{2}x$)
2. For $-1.5(-3 + 4n + 8.2)$: $\boldsymbol{-7.8 - 6n}$