e Notice that there is the same number on both sides of the symbol.
F
f What does the symbol < mean?
A
a Always
B
b Sometimes
C
c Never
D
d Sometimes
E
e Always
F
f Never
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 - 4 is less than 9. Since the relation is less than, we can also say that it is less than or equal to. This relation can also be written as - 4 ≤ 9, so the given statement is always true.
b The given statement, x<1, means that x is less than 1. We want to determine whether it is sometimes true, always true, or never true. Since we do not know the value of x, let's graph the inequality on a number line to find the values of x that satisfy it.
As we can see, the inequality creates a true statement only for some values of x — for those less than 1. Thus, the statement is sometimes true.
c 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 - 5 is less than - 2, so the given statement is never true.
The solution to the equation is x=- 1. It means that the given statement is true only if x equals - 1. Any other time the statement is false. Therefore, the given statement is sometimes true.
e Let's take a look at the given statement.
61=61
Notice that on both sides of the symbol we have the same number, which is 61. Therefore, both sides of the given equation are equal, and the given statement is always true.
f Recall that the symbol < means less than.
- 6? <- 6
Notice that on both sides of the symbol we have the same number, which is - 6. Thus, both sides of the given inequality are equal, and it is not true that number on one side of the inequality is less than number on the other side. Therefore, the given statement is never true.
