Chapter 1.4, Problem 43IP

To determine

Translate the verbal expression into an algebraic expression, then simplify it, the sum of two times a number and five added to six times a number.

Answer to Problem 43IP

  $\left(2x+5\right)+6x;8x+5$

Explanation of Solution

Given:

The sum of two times a number and five added to six times a number.

Concept Used:

Associative property of Addition

  $a+\left(b+c\right)=\left(a+b\right)+c$

In order to translate the verbal expression into an algebraic expression, then simplify it, the sum of two times a number and five added to six times a number, first let the number be x then the sum two times a number and 5 implies that adding 5 and 2 times x and then adding 6 times the number x , so the expression is as shown below:

  $\left(2x+5\right)+6x$

Now, simplify the above equation by using associative property of addition as shown below:

  $\begin{array}{l}\left(2x+5\right)+6x\\ =\left(2x+6x\right)+5\\ =8x+5\end{array}$

So, the algebraic expression is $\left(2x+5\right)+6x$ , and the simplification is $8x+5$.