The phrase is at most divides the sentence into what should be on the left-hand side and what should be on the right-hand side of the inequality.
Inequality: x * 5 ≤ 30 Solution: x ≤ 6
Practice makes perfect
We are given a verbal expression and we want to write an inequality that it represents.
The product of a number and fiveis at most 30
Every inequality has an inequality symbol and values or expressions on either side of this symbol. In this exercise, we have the phrase is at most, so we can identify that the inequality symbol should be ≤.
The product of a number and five ≤ 30
On the left-hand side, we have one key phrase: The product. These words tell us the operations that will be used in our inequality. The product indicates multiplication. After this phrase, we have two things: a number, which we can write as a variable x, and five, which we can write as 5.
The product of a number and five
x * 5
On the right-hand side of the inequality symbol we have a constant 30. Putting these sides together, we have a complete inequality.
The product of a number and five is at most 30
x * 5 ≤ 30
Finally, we want to solve this inequality. Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when we divide or multiply by a negative number, we must reverse the inequality sign.
