Chapter 1.4, Problem 47IP

To determine

Translate the verbal expression into an algebraic expression, the sum of four times a number and seven less than two times the number.

Answer to Problem 47IP

  $4x+\left(2x-7\right);6x-7$

Explanation of Solution

Given:

The sum of four times a number and seven less than two times the 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 four times a number and seven less than two times the number, first let the number be x then the sum of four times a number and seven less than two times the number, implies that adding 2 times x minus 7 and 4 times x , so the expression is as shown below:

  $4x+\left(2x-7\right)$

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

  $\begin{array}{l}4x+\left(2x-7\right)\\ =\left(4x+2x\right)-7\\ =6x-7\end{array}$

So, the algebraic expression is $4x+\left(2x-7\right)$ , and the simplification is $6x-7$.