Chapter 8.7, Problem 61HP

To determine

To write a real-world problem involving an inequality and negative numbers where the inequality symbol won’t reversed while finding the solution.

Answer to Problem 61HP

The price of a CD after a discount of $ 1.5 was at most $9. Find the original price of the CD.

Explanation of Solution

Calculation:

Let the original price of the CD be x .

Then after a discount of $1.5, the discounted price was at most $9, that is less than or equal to 9. So, using the inequality it can be expressed as

  $x+\left(-1.5\right)\le 9$

This is an inequality involving the negative numbers.

Now to solve it further add 1.5 both sides and simplify further as

  $\begin{array}{c}x+\left(-1.5\right)\le 9\\ x-1.5\le 9\\ x-1.5+1.5\le 9+1.5\\ x\le 10.5\end{array}$

On solving the inequality, it won’t change the sign of the inequality.