Chapter 7.5, Problem 50IP

To determine

Write an expression in factored form that is equivalent to the given expression $\frac{5}{6}x-30$ .

Answer to Problem 50IP

  $\frac{5}{6}x-30=\frac{5}{6}(x-36)$

Explanation of Solution

Given:

The expression: $\frac{5}{6}x-30$

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: $\frac{5}{6}x-30$

  $\frac{5}{6}x-30=\frac{5}{6}·x-\frac{5}{6}·6·6=\frac{5}{6}(x-36)[\text{GCF}=\frac{5}{6}]\text{and}[30=36·\frac{5}{6}]$

Thus, $\frac{5}{6}x-30=\frac{5}{6}(x-36)$