You can use an inequality to compare any two numbers by writing specific symbols to show which number is greater than or less than the other. While you can use inequalities to compare any kind of numbers, here you will use inequalities to compare integers.
Remember:
Integers are the positive and negative numbers that do not have fractional parts. The number 0 is also an integer.
Sometimes the integers are defined as the set of whole numbers and their opposites. In this definition, the number 0 is still included as an integer.
Look at the example shown.
Noor and her committee overspent the paper plates and cups budget by $2, but they have $4 left in their refreshments budget.
You can express these integers as −$2 and $4.
Write an inequality using the symbol < to compare the integers −2 and 4.
The steps on the tabs below explain how to write an inequality to compare two integers. Click each tab and read the information given. Answer the questions you find as you read. The last tab in the set contains a video example. As you watch that example, pay close attention to how the instructor uses the steps to create her inequality.
You may want to use the study guide to follow along. If so, click below to download the study guide.
Draw a horizontal number line, and plot the given integers along it. Remember, the value of integers increases as you move to the right along the number line.
A horizontal number line from −5 to 5 in increments of 1. There are two points plotted. One is at −2 and the other is at 4.
The integers −2 and 4 are plotted on this number line.
You need to write an inequality using a less than (<) symbol.
Look at the number line.
Identify which integer is smallest.
A horizontal number line from -5 to 5 in increments of 1. There are two points plotted. One is at -2 and the other is at 4.]
Write the inequality.
You saw on the number line that the integer −2 is smaller than the number 4.
Using the symbol <, the inequality is \( -2 \lt 4 \).
Can you write an inequality using the integers −2 and 4 using the greater than (>) symbol? If so, write the inequality. If not, explain why not. Click the answer button to check your response when you are ready.
You can write the inequality 4 > −2 because the integer 4 is further to the right on a horizontal number line than −2. This means that 4 is larger than −2.
When you write inequalities, remember that the symbol always opens to the larger number.
Let's Watch
Watch the tutorial below to see more examples of writing inequalities using integers.
Let's work through examples of writing inequalities.
1. Write an inequality that compares −15 and −8 using the ≥ symbol.
To compare these integers, I will plot them on a number line. I'll draw a straight line with arrows on each end. Both integers are negative, so I only need the negative part of my number line. I'll put 0 here. I will use a scale of 3; −3,−6 −9,−12,−15. Now I go to −8, which will be about here, and I will plot −8. Then I will go to −15 which goes right here on the −15 tick mark, and I will plot −15.
I can look at the placement of the integers on the number line to compare them. I'm using the ≥ symbol. Since −8 is closer to 0 than −15 is, it is greater than −15. To compare using the greater than or equal to symbol we would have −8 ≥ −15.
2. Yesterday the temperature was \( -11^\circ F \), and today it was \( 0^\circ F \). Was it warmer today or yesterday?
To determine the warmer day, I will plot these degrees on a number line. I will create a number line that has 0 and −11 on it. I'll make tick marks. And now I will plot the two degrees. −11 goes right on the −11 tick mark, and 0 goes right on the 0 tick mark.
Since −11 is to the left of 0, we know that it is less than 0 and 0 is greater than −11. This means 0 > −11, therefore it was warmer today.
Together we have worked through examples of writing inequalities. Refer to this video if you need help when working on these types of problems.
Question
While watching the video, you wrote the inequality −8 ≥ −15 to compare the integers −15 and −8.
Now use the symbol < to compare the integers −15 and −8. Use the number line to explain why you wrote your inequality as you did.
−15 < −8
The integer −15 is further to the left on the number line than −8, so it is smaller than the integer −8.
A horizontal number line from −17 to 0 in increments of 1. There are two points plotted. One is at −15 and the other is at −8.
