Question

Which of the following is not an equivalent form of the compound inequality

x - 1 < -10 or x + 12 > 12

A number line with an open circle on -9, an open circle on 0, and shading in between.

x < -9 or x > 0

A number line with an open circle on -9, shading to the left, and an open circle on 0, shading to the right.

x > 0 or x < -9

My answer is x > 0 or x < -9

Is this right?

Answer 1

@whpalmer4

Answer 2

Well, let's test it out, shall we?

Our original inequality is
\[x-1<-10 \text{ or } x+12 >12\]
We can rearrange those a bit to make them simpler. We'll add 1 to both sides for the left one, and subtract 12 from both sides for the right one, giving us
\[x<-9 \text{ or } x > 0\]

That looks awfully similar to your answer choice, doesn't it? But we're supposed to find one that is not equivalent.

Answer 3

Going further, we can see that we'll have open circles on x = -9 and x = 0. The question is, do we shade between the circles or outside them? We'll pick a point in the middle and try it out. If it satisfies the inequality, then the middle part is shaded, otherwise the outside part is shaded. Let's try x = -5:
-5 < -9 false
-5 > 0 also false
so it appears that we shade the area to the left of x=-9 and to the right of x = 0.

With those facts in hand, which answer will you choose?