Chapter 8.2, Problem 84CCR

To determine

An equation and solve the equation to find the record low temperature

Answer to Problem 84CCR

The equation is $106-x=128$ .

The record low temperature is $x=-22$

Explanation of Solution

Given:

The difference between the record and low temperatures in Columbus, Ohio, is ${128}^{\circ }F$ . The record high temperature is ${106}^{\circ }F$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

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.

Calculation:

In order to find the equation here let’s assume that the low temperature is x and according to the question high temperature is ${106}^{\circ }F$ and the difference is ${128}^{\circ }F$

Thus, the equation is shown below,

  $106-x=128$

Thus, the equation is $106-x=128$ .

In order to solve the equation first subtract both sides by $106$ and then simply further as below:

  $\begin{array}{c}106-x=128\\ 106-x-106=128-106\\ -x=22\\ \Rightarrow x=-22\end{array}$

Thus, the record low temperature is $x=-22$