Try to compare the numbers in each inequality on a number line. It is usually easier to compare numbers when they are written in the same format.
A
Practice makes perfect
We are given four inequalities and want to determine which of them is not true.
Option
Inequality
True or False?
A
4 12> 25/4
?
B
-4 12> -25/4
?
C
-6< -5
?
D
-1/2< 1/2
?
Let's first analyze the inequalities from options C and D
C and D
To determine if the inequalities from options C and D are true, we will plot all the numbers on a number line.
We can see that -6 is to the left of -5 and that - 12 is to the left of 12. Therefore, -6 is less than -5 and - 12 is less than 12.
Option
Inequality
True or False?
A
4 12>25/4
?
B
-4 12>-25/4
?
C
-6<-5
True
D
-1/2<1/2
True
We found that both inequalities are true.
B
In option B, we are given the following inequality.
- 4 12>-25/4
It is usually easier to compare numbers when they are written in the same format, so let's rewrite the right-hand side of the inequality as a mixed number.
Now we can write compare the numbers on a number line.
We can see that -4 12 is to the right of -6 14, which is equal to - 254. This means that -4 12 is greater than - 254.
Option
Inequality
True or False?
A
4 12>25/4
?
B
-4 12>-25/4
True
C
-6<-5
True
D
-1/2<1/2
True
A
Let's find out if the equality from option A is true.
4 12>25/4
Similarly to before, we will rewrite the fraction on the right-hand side of the inequality as a mixed number.
25/4=6 14
Now we can compare the numbers on a number line.
We can see that 4 12 is to the left of 6 14, which is equal to 254. This means that 4 12 is less than 254.
4 12>25/4 âś“ [0.8em]
4 12<25/4 *
This means that the inequality from option A is not true.
