It might help to replace m with some positive number. Let's say m = 5
So everywhere you see an 'm', in an inequality or a graph, replace it with 5. You can pick any other positive number if you prefer.
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Inequality a.
x/m < -1
x/5 < -1 ... replace m with 5
x < -5 ... multiply both sides by 5
The graph will have an open circle at -5 and shading to the left
This describes graph C after you replace m with 5.
Note: if m = 5, then -m = -5.
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Inequality b.
x/m > 1
x/5 > 1
x > 5
We'll have an open circle at 5 with shading to the right. This describes graph A.
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Inequality c.
x/m < 1
x/5 < 1
x < 5
This describes graph B since it has an open circle at 5 and shading to the left.
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Inequality d.
-x/m < 1
-x/5 < 1
x > -5 .... inequality sign flips when we multiply both sides by a negative number
The graph would be graph D because there is an open circle at
-m = -5
and we shade to the right of this open circle.
