MHB Is the inequality correctly solved by multiplying each fraction by 100?

[mathdad]

Solve the inequality.

(9/10) < (3x - 1)/-2 < 91/100

Do I start by multiplying each fraction by 100?

 

[HallsofIvy]

That would be one reasonable way of starting. As is so often the case, you can, you don't have to. And, since 100 is positive, multiplying by 100 does not change the direction of the inequalities: 90< -50(3x- 1)< 91.

But that "-" in the "-2" is going to cause problems!
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[mathdad]

90< -50(3x- 1)< 91

90 < -150x + 50 < 91

90 < -150x < 91 - 50

90 < -150x < 41

-90/150 > x > -41/150

-3/5 > x > -41/150

Correct?