a Plot both numbers on a number line. The greater number is further to the right.
B
b What does the symbol ≥ mean?
C
c Plot both numbers on a number line. The greater number is further to the right.
D
d What does the symbol ≤ mean?
E
e Plot both numbers on a number line. The greater number is further to the right.
F
f What does the symbol > mean?
G
g Plot both numbers on a number line. The greater number is further to the right.
H
h Plot both numbers on a number line. The greater number is further to the right.
A
a False.
B
b True.
C
c True.
D
d True.
E
e True.
F
f False.
G
g True.
H
h False.
Practice makes perfect
a We can compare these two numbers by plotting them on a number line. The greater number will be further to the right.
Based on this number line graph we can tell that 11 is greater than -13, so the given statement is false.
b Before we compare numbers to decide whether the given statement is true, let's simplify the left-hand side of the inequality.
5(2)≥?10⇒10≥?10
Recall that the symbol ≥ means greater than or equal to.
Notice that on both sides of the symbol we have the same number, which is 10. Thus, both sides of the given inequality are equal, and the given statement is true.
c Before we will compare numbers to decide whether the given statement is true, let's simplify the right-hand side of the inequality.
We can compare these two numbers by plotting them on a number line. The greater number will be further to the right.
Based on this number line graph, we can tell that 13 is greater than 12. This relation can also be written as 13>12, so the given statement is true.
d Recall that the symbol ≤ means less than or equal to.
4≤?4
Notice that on both sides of the symbol we have the same number, which is 4. Thus, both sides of the given inequality are equal, and the given statement is true.
e We can compare these two numbers by plotting them on a number line. The greater number will be further to the right.
Based on this number line graph, we can tell that 9 is greater than -9. Since the relation is greater than, we can also say that it is greater than or equal to. This relation can also be written as 9≥-9, so the given statement is true.
f Recall that the symbol > means greater than.
-2>?-2
Notice that on both sides of the symbol we have the same number, which is -2. Thus, both sides of the given inequality are equal, and it is not true that the number on one side of the inequality is greater than the number on the other side. Therefore, the given statement is false.
g We can compare these two numbers by plotting them on a number line. The greater number will be further to the right.
Based on this number line graph, we can tell that -16 is less than -15. This relation can also be written as -16<-15, so the given statement is true.
h We can compare these two numbers by plotting them on a number line. The greater number will be further to the right.
Based on this number line graph, we can tell that 0 is less than 6, so the given statement is false.
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