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1.5 A) Inequalities Introduction
1.5 A) Inequalities Introduction
Inequalities are symbols that compare two values. There are four different inequalities; <, >, ≤ and ≥. Here are the definitions of what these inequalities mean:
I think that the easiest way to remember what an inequality sign means is to remember that the smaller number in the inequality is on the point of the inequality (point means smaller number) and the larger number in the inequality is on the side of the inequality that is larger (the side of the inequality that has a gap between the two lines). For the inequality <, the smaller number would be on the left and the larger number would be on the right. And for the inequality >, the smaller number would be on the right and the larger number on the left. The next thing to remember is that if there is a line under the inequality, it means that “or equal to” is included in the inequality. This is the case for ≤ and ≥.
It does not matter the way that we write the inequality. For example, if we had the variable e and e was less than or equal to 12, we can write this as:
- < – this is the “less than” symbol. It means that the number on the left of the inequality is smaller than the number on the right of the inequality. For example, the inequality could be a < 8, and this means that the unknown value a is less than 8. We do not know what the value of a is, we just know that it is less than 8. For example, a could be 5, -6, -205 etc.
- > – this is the “greater than” symbol. It means that the number on the left of the inequality is greater than the number on the right of the inequality. For example, if we had the inequality b > 12, it would mean that the unknown value b is greater than 12. For example, b could be 13, 40, 1923 etc.
- ≤ – this is the “less than or equal to” symbol. It means that the number on the left of the inequality is less than or equal to the number on the right of the inequality. For example, if we had the inequality c ≤ 20, the value of c could be equal to 20 or less than 20; c could be 20, 5, -99 etc.
- ≥ – this is the “greater than or equal to” symbol. It means that the number on the left of the inequality is greater than or equal to the number on the right of the inequality. The inequality d ≥ 14, would mean that the value of d can be greeter or equal to 14; d could be 14, 65, 194 etc.
I think that the easiest way to remember what an inequality sign means is to remember that the smaller number in the inequality is on the point of the inequality (point means smaller number) and the larger number in the inequality is on the side of the inequality that is larger (the side of the inequality that has a gap between the two lines). For the inequality <, the smaller number would be on the left and the larger number would be on the right. And for the inequality >, the smaller number would be on the right and the larger number on the left. The next thing to remember is that if there is a line under the inequality, it means that “or equal to” is included in the inequality. This is the case for ≤ and ≥.
It does not matter the way that we write the inequality. For example, if we had the variable e and e was less than or equal to 12, we can write this as:
Or we could write it as.
Both of these inequalities are saying the same thing.
A few Examples
We are now going to have a look at a few examples where we are asked to put the correct inequality sign between two numbers.
Example 1
Put the correct inequality sign in the box below.
We are now going to have a look at a few examples where we are asked to put the correct inequality sign between two numbers.
Example 1
Put the correct inequality sign in the box below.
We work out the appropriate inequality sign by comparing the two numbers. The two numbers involved are 34 and 89. 34 is less than 89, which means that we put < in the box. The answer is:
Example 2
Put the correct inequality sign in the box below.
Put the correct inequality sign in the box below.
Like the question before, we find the correct inequality sign by comparing the two numbers. 74 is greater than 6, which means that we put a > in the box. The answer is:
Example 3
Put the correct inequality sign in the box below.
Put the correct inequality sign in the box below.
This question is a little trickier because the numbers involved are both negative. You may find it easier to answer this question by drawing a quick number line and marking the two numbers on the number line. You only need to do a very quick sketch of the number line. The number line with -45 and -8 is shown below.
On the above number line, the numbers on the left are the smallest/ lowest and the numbers on the right are the largest/ greatest. -45 is on the left of -8, which means that -45 is less than -8. Therefore, the inequality sign that goes into the box is <. The answer is:
Example 4
Put the correct inequality sign in the box below.
Put the correct inequality sign in the box below.
Like the question before, both of the numbers are negative. Therefore, I am going to draw these two numbers on a number line. The number line is shown below:
From looking at the above number line, we can see that -4.8 is on the right of -6.3. This means that -4.8 is greater than -6.3. Therefore, the inequality that goes in the box is >. The answer is shown below.