Chapter 8, Problem 17CR

To determine

Translate into an equation and solve

Answer to Problem 17CR

The equation is $2x-6=-22$

The number is $x=-8$

Explanation of Solution

Given:

Six less than twice a number is $-22$

Concept Used:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

In order to translate the sentence into an equation

Let x be the number since six less than twice a number is $-22$ means that as shown below,

  $2x-6=-22$

Thus, the equation is $2x-6=-22$

In order to solve the equation $2x-6=-22$ first add both sides by $6$ and then divide both sides by $2$ and then simplify further as below:

  $\begin{array}{c}2x-6=-22\\ 2x-6+6=-22+6\\ 2x=-16\\ \frac{2x}{2}=\frac{-16}{2}\\ x=-8\end{array}$

Thus, the number is $x=-8$