The number line below shows information about a variable, m. Select all of the following values that m could take: -2, 4, -3.5, 0, -5, -7.

Understand the Problem

The question is asking for all possible values that the variable 'm' could take based on the information provided in the number line. It lists several numerical options and requires the user to select which of those fall within the range shown on the number line.

Answer

The values that $ m $ could take are $-2$, $-3.5$, $0$, and $-5$.

Steps to Solve

Identify the Range on the Number Line The variable ( m ) must fall within the range indicated on the number line. In this case, the number line appears to show that ( m ) is between (-5) and ( 2 ).
Determine the Inclusion of the Endpoints To determine which values are included, check if ( m ) can be equal to (-5) and ( 2). If the endpoints are solid (or closed), then those values are included. Here, (-5) is included but ( 2 ) is not since the arrow does not reach it.
List Possible Values of ( m ) From the range, we have: $$ -5 \leq m < 2 $$

Now we list the given values:

(-2)
(4)
(-3.5)
(0)
(-5)
(-7)

Check Each Value Against the Range Now check each of these values to see if they fall within the range:

(-2) is within the range.
(4) is outside the range.
(-3.5) is within the range.
(0) is within the range.
(-5) is included.
(-7) is outside the range.

Select All Valid Values The final valid values of ( m ) are those that fall within ([-5, 2)), which are:

(-2)
(-3.5)
(0)
(-5)

The possible values that ( m ) could take are (-2), (-3.5), (0), and (-5).

More Information

In this problem, the number line indicates a range of values for ( m ). This exercise helps illustrate how to interpret ranges and inequalities visually.

Tips

A common mistake is to overlook the endpoint. Remember to check if the endpoints are included or not.
Confusing positive and negative values can also lead to incorrect selections.

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