Question

Let m > 0. Match each inequality with its graph.

Answer 1

the correct pairings are:

• inequality a, graph C.
• inequality b, graph A.
• inequality c, graph B
• inequality d, graph D.

How to match each inequality with its graph?

Here we know that m > 0, now let's look at the first inequality:

x/m < -1.

if x = -m, we will have:

-m/m < - 1

-1 < 1

This is false, then x must be a value smaller than -m, then we need to draw a open circle at -m and shade al the region to the left of it, this is what we can see in graph C.

b) Now the inequality is:

x/m > 1.

Similarly as before, this time we evaluate in x = m.

m/m > 1

1 > 1

From this, we can see that x must be larger than m, then we will have an open circle at x = m and we need to shade al the region to the right of m.

This is what we see in graph A.

c) This inequality is:

x/m < 1

This is almost the same as the case above, this time we shade to the left instead of the right, so the correct option is graph B.

d) This is:

-x/m < 1

If we multiply both sides by -1 we get:

x/m > -1

This is the opposite of what we get in inequality "a", but this time we need to shade the right side of -m, this is what we see in graph D.

Concluding, the correct pairings are:

inequality a, graph C.

inequality b, graph A.

inequality c, graph B

inequality d, graph D.

If you want to learn more about inequalities:

brainly.com/question/24372553

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