Recall the use and meaning of the inequality symbols.
See solution.
Practice makes perfect
When working with inequalities in word problems, it is common to have the expressions no more than and no less than. Let's discuss a little on how to interpret these phrases in this context and how we can represent them algebraically.
No More Than
The phrase no more than gives us the upper limit. This is the maximum value the variable can take. We represent this using the symbol ≤, which is read as less than or equal to.
A number no more than 5
x ≤ 5
In this case, the variable x can take all values lower than 5, including 5 itself. A real-life example of this phrase could be about the number of passengers that can fit in a car.
My car can fit no more than 5 people.
This sentence means that 5 people can safely ride in the car, but 5 is the maximum.
No Less Than
On the other hand, no less than tells us about the lower limit. This sets a minimum value for our variable. We represent this using the symbol ≥, which is read as greater than or equal to.
A number no less than 10
x ≥ 10
In this case, the variable x can take all values greater than 10, including 10 itself. A real-life example of this phrase could be the number of people required for a group discount.
We need no less than 10 people if we want the group discount on bowling.
This sentence tells us that the price per game is cheaper if 10 or more people go bowling together.
