Chapter 3.4, Problem 24P

Open-Ended Write two different inequalities that you can solve by adding 2 to each side and then dividing each side by $-12.$

Solve each inequality.

To determine

To solve:Two inequalities which satisfies the given conditions

Answer to Problem 24P

The inequalities are $12x-2\le 10$ and $12y-2>22$

The solutions are $x\le 1$ and $y>2$ respectively.

Explanation of Solution

Given:

Write two different inequalities that can be solved by adding 2 to each side and then dividing each side by -12

Calculation:

Let us consider the two inequalities as follows:

  $12x-2\le 10$ and $12y-2>22$

Solving the first inequality:

  $\begin{array}{l}12x-2\le 10\\ =>12x-2+2\le 10+2[Adding2onbothsides]\\ =>12x\le 12\\ =>x\le 1[Dividing12onbothsides]\end{array}$

Solving the second inequality:

  $\begin{array}{l}12y-2>22\\ =>12y-2+2>22+2[Adding2onbothsides]\\ =>12y>24\\ =>y>2[Dividing12onbothsides]\end{array}$