Chapter 7.1, Problem 23IP

To determine

To simplify the expression $-\frac{1}{2}\left(n+4\right)$ .

Answer to Problem 23IP

  $-\frac{1}{2}n-2$

Explanation of Solution

Given information:

The expression, $-\frac{1}{2}\left(n+4\right)$

Concept used:

• The distributive property of binomials (FOIL): $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$
• Left Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$
• Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression $-\frac{1}{2}\left(n+4\right)$ , first use the distributive property to expand the parenthesis and then simplify further by using the exponent property as shown below

  $\begin{array}{c}-\frac{1}{2}\left(n+4\right)=-\frac{1}{2}\left(n+4\right)\\ =-\frac{1}{2}\left(n\right)+\left(-\frac{1}{2}\right)\left(4\right)\\ =-\frac{1}{2}n-2\end{array}$

Thus, the given expression simplifies to $-\frac{1}{2}n-2$ .