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.
Example Inequality: g÷ (- 4)≤ 5 Solution: g≥ - 20
Practice makes perfect
We want to write the word sentence as an inequality and the solve it. We can do each of these things one at a time.
Word Sentence
Let's consider the given verbal expression!
The quotient of a numberg and - 4 is at most5Every 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 quotient of a numberg and - 4 ≤ 5
On the left-hand side, we have one key phrase: quotient of ... and ... These words tell us the operations that will be used in our inequality. Quotient of ... and ... indicates division.
The quotient of a numberg and - 4
g ÷ - 4
On the right-hand side, we have a constant. Putting these sides together, we have a complete inequality.
The quotient of a numberg and - 4 is at most 5
⇕
g ÷ - 4 ≤ 5
Solving the Inequality
We want to solve the given inequality. In this case, we can use the Multiplication Property of Inequality. Let's multiply both sides of the inequality by - 4!
