Answer: 1D, 2E, 3B, 4A, 5C
Step-by-step explanation:
First, eliminate choices that cannot go together.
The "greater than" and "less than" symbols, represented by > and <, are used to show that a number is greater than another set of numbers, but not equal to the set of numbers.
The "greater than or equal to" and "less than or equal to" symbols, represented by ≥ and ≤, are used to show that a number can also be equal to a set of numbers.
On the number line, open dots are used to represent > and <.
Closed dots are used to represent ≥ and ≤.
Using this, C, D, and E must match with 1, 2, and 5.
Dealing with 3 now:
4m ≥ 32
Divide both sides by 4 to simplify m:
m ≥ 8 - This is used to show that m is greater than or equal to 8.
This lines up with choice B: the line starts at 8 and goes onwards to positive infinity.
This means that 4 matches to A, because it is the only other option with a closed dot.
Looking at 1 (x - 5 < 2), we can simplify it very easily by adding 5 to both sides of the inequality:
x < 7 - This is used to show that x is less than 7.
This lines up with choice D: The line starts at less than 7 and goes downwards to negative infinity.
Looking at 2 (m + 24 > 20), we can do this the same way. Subtract 24 from both sides to get:
m > -4 - This is used to show that m is greater than negative 4.
This lines up with choice E: The line starts at greater than 4 and goes to positive infinity.
The last choice, choice 5, must match with choice C.
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