The phrase is no more than 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 - 21 12 ≤ 14 14 Solution: x ≤ 35 34
Practice makes perfect
We are given a verbal expression and we want to write an inequality that it represents. Then, we will solve the inequality.
The difference between a number and21 12 is no more than14 14.
Let's start by defining a variable. We can name a number in the sentence as x.
The difference between xand21 12 is no more than14 14
Every inequality has an inequality symbol and values or expressions on either side of this symbol. In this exercise, we have the phrase no more than, so we can identify that the inequality symbol should be ≤.
The difference betweenxand21 12 ≤ 14 14
On the left-hand side, we have one key phrase: the difference between. These words tell us the operations that will be used in our inequality. The difference between indicates subtraction.
The difference between x and 21 12
x - 21 12
On the right-hand side, we have a constant. Putting these sides together, we have a complete inequality.
x - 21 12 ≤ 14 14
Finally, we can solve the inequality. To do so, we will use the Addition Property of Inequality. This will eliminate the addition and isolate x.
