If -3

Question

If -3 <_ x <_ -1, determine a and b for the inequality:

a <_ 6 - 2x < b

I'm totally unsure how a question like this works, considering I need to flip the inequalities to get the "-2x" part of the question.

anonymous · Answer

Multiply everything by -2 then add 6

anonymous · Answer

The flipping of the sign doesn't matter, it just means that your a and b are on different sides

anonymous · Answer

$$-3*-2\ge-2x \ge-1*-2$$
$$12\ge6-2x \ge8$$

anonymous · Answer

So your a is 8 and b is 12

anonymous · Answer

Ah, okay, thanks.

anonymous · Answer

What about the < vs. the <_?  The answer you gave had two "greater than or equal" signs, shouldn't there be a "greater than" sign in there, a reflection of the "<" in the initial question?

anonymous · Answer

Oh yes I missed that. Signs shouldn't usually change mid equation but if it's smaller or equal to 12, then it must be smaller than anything larger than 12, so I guess you could write that