Chapter 7.5, Problem 47IP

To determine

Write an expression in factored form that is equivalent to the given expression $\frac{1}{2}x+4$ .

Answer to Problem 47IP

  $\frac{1}{2}x+4=\frac{1}{2}(x+8)$

Explanation of Solution

Given:

The expression: $\frac{1}{2}x+4$

Concept Used:

To find the factor of the expression:

Step 1: find the GCF of the expression and take out the GCF from each term of the expression and write in factor form.

Example: The expression $ab+ac$ , $a$ is the GCF of the expression. Take out the GCF and write in factor form: $ab+ac=a·b+a·c=a(b+c)$

Calculation:

Find the factor of the expression: $\frac{1}{2}x+4$

  $\frac{1}{2}x+4=\frac{1}{2}·x+\frac{1}{2}·2·2·2=\frac{1}{2}(x+8)[\text{GCF}=8]\text{and}[4=8·\frac{1}{2}]$

Thus, $\frac{1}{2}x+4=\frac{1}{2}(x+8)$