Chapter 1.4, Problem 44IP

To determine

Translate the verbal expression into an algebraic expression, then simplify it, eight more than six times a number added to one more than nine times the number.

Answer to Problem 44IP

  $\left(\left(6x+9x\right)+1\right)+8;15x+9$

Explanation of Solution

Given:

eight more than six times a number added to one more than nine 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, eight more than six times a number added to one more than nine times the number, first let the number be x then eight more than six times a number added to one more than nine times the number implies that adding 6 time a number and 9 times a number then adding 1 and 8 on it, so the expression is as shown below:

  $\left(\left(6x+9x\right)+1\right)+8$

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

  $\begin{array}{l}\left(\left(6x+9x\right)+1\right)+8\\ =\left(6x+9x\right)+\left(1+8\right)\\ =15x+9\end{array}$

So, the algebraic expression is $\left(\left(6x+9x\right)+1\right)+8$ , and the simplification is $15x+9$.