Question

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?

Answer 1

The inequality sign stays the same when multiplying both sides by a positive constant. The solution uses <= because Michael cannot send more than a third of his salary. The maximum possible salary for Michael is $3000.

Step-by-step explanation:

a. The inequality sign stays the same because multiplying both sides by a positive constant (in this case, 3) does not change the order of the numbers. It only scales the values.

b. The circumstances that would change or flip the inequality sign are when you multiply or divide both sides by a negative constant. In this case, you would need to flip the inequality sign.

2. The solution uses the inequality <= because Michael cannot send more than a third of his salary. Using <= ensures that he can send an amount less than or equal to one-third of his salary.

3. From the solution, the maximum possible salary for Michael is $3000.

4. The four types of inequalities are:

1. Less than (<)
2. Greater than (>)
3. Less than or equal to (<=)
4. Greater than or equal to (>=)