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:
t ÷ 32≤ 4.25 Solution: t ≤ 136
Practice makes perfect
We are given a word sentence and we want to write an inequality that it represents.
A number t divided by 32 is at most 4.25.
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 ≤.
A number t divided by 32 ≤ 4.25.
On the left-hand side, we have the phrase A number t divided by 32. These words tell us that t is a variable symbol and that the operation that will be used in our inequality is the division. This is because of the word divided.
A number t divided by 32 ≤ 4.25.
t ÷ 32 ≤ 4.25
On the right-hand side, we have the constant 4.25. If we put these sides together, we have a complete inequality.
A number t divided by 32 is at most 4.25.
t ÷ 32 ≤ 4.25
Now let's solve this inequality. Remember that 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.
