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.

Answer 1

Multiply everything by -2 then add 6

Answer 2

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

Answer 3

\[-3*-2\ge-2x \ge-1*-2\]
\[12\ge6-2x \ge8\]

Answer 4

So your a is 8 and b is 12

Answer 5

Ah, okay, thanks.

Answer 6

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?

Answer 7

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