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

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SUMMARY

The inequality (9/10) < (3x - 1)/-2 < 91/100 can be solved by multiplying each fraction by 100, which maintains the direction of the inequalities due to the positive multiplier. The transformation leads to the expression 90 < -50(3x - 1) < 91. Simplifying this results in the inequality -3/5 > x > -41/150, confirming the correct solution for x.

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mathdad
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Solve the inequality.

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

Do I start by multiplying each fraction by 100?
 
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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!
​
 
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?
 

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