Chapter 1.6, Problem 23PPE

To determine

To write: the algebraic expression for given verbal expression and then to simplify.

Answer to Problem 23PPE

The expression is $4(2x+6)$ and is simplified to $8x+24$

Explanation of Solution

Given information:

Consider the “ $4$ times the sum of $2$ times x and $6$ ”

Calculations:

Write the expression

  $2$ times x $\Rightarrow 2x$

sum of $2$ times x and $6$

  $\Rightarrow 2x+6$

  $4$ times the sum of $2$ times x and $6$

  $\Rightarrow 4(2x+6)$

Simplify the expression

  $\begin{array}{l}4(2x+6)=4\cdot (2x)+4\cdot 6\text{ distributive property }\\ =8x+24\end{array}$

Hence, the expression is $4(2x+6)$ and is simplified to $8x+24$