Chapter 1.2, Problem 33E

To determine

To solve: Write and solve the equation and find the number.

Answer to Problem 33E

The required number is -22.

Explanation of Solution

Given information:

Six times the sum of a number and 15 is -42.

Solution:

Let a number be x.

According to the question ,

Sum of a number x and 15 = $\left(x+15\right).$

Six times the sum of a number and 15 = $6\left(x+15\right)$ .

Therefore, statement “Six times the sum of a number and 15 is -42” could be represented an equation as:

  $6\left(x+15\right)=-42$

Now, let us simplify above equation for unknown number x.

  $6x+90=-42$

Subtract 90 from both side of the equation

  $6x+90-90=-42-90$

  $\Rightarrow 6x=-132$

Divide by 6 on both side

  $\frac{6x}{6}=-\frac{132}{6}$

  $\Rightarrow x=-22$

Therefore, the number unknown is -22.