Problem: Michael wants to send some money to his family but he cannot send more than a third of his salary. If he sent $1000 to his family, then what is the maximum possible value for his salary?

Solution:

Let Michael’s salary be x.

From the Question, he CANNOT send more than a third of his salary.

One-third of Michael's Salary is 1/3 x

He sent $1000 to his family. Since he can send an amount that is less than 1/3
of his salary, we have the following:

1/3 x<=$1000

Multiplication property for inequality says: when a positive constant or variable is multiplied or divided on both sides of the inequality, it keeps the inequality equation the same.

To remove the 3 from the denominator, multiply both sides by 3

1/3 x*3<=$1000*3

x<=$1000*3

x<=$3000

Now answer the following Questions:

1. From the solution, we see that 3 is multiplied on both sides, but the inequality sign is not changed/flipped.

a. Why does the inequality sign stay the same?

b. What are the circumstances that would change/flip the inequality sign?

2. Why does the solution use inequality <= _?

3. From the solution what can be the maximum possible salary for Michael?

4. What are the four types of Inequalities?