Chapter 8.1, Problem 48HP

To determine

His mistake and correct

Answer to Problem 48HP

he should have multiplied each sides by 4

Explanation of Solution

Given:

Sam is solving $\frac{1}{4}x=-20$

  

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.

In order to find the mistake, we see that in the solution Sam divide each sides by 4.

Let’s correct the equation $\frac{1}{4}x=-20$ below:

  $\begin{array}{c}\frac{1}{4}x=-20\\ \frac{1}{4}x\times 4=-20\times 4\\ x=-80\end{array}$

Thus, he should have multiplied each sides by 4