Math CentralQuandaries & Queries


Question from Courtney, a student:

What is the answer to -5x < 25+10

Hi Courtney.

With "inequalities" (that's where you have an equation with greater-thans or less-thans involved), you work the same way as you do with normal equations with just equal signs, except that you have to be careful because some operations "flip" the direction (from less-than to greater-than or vice-versa). The most obvious situation is when you multiply or divide by a negative. This flips the inequality.

Here's an example:

Solve: 10-3x ≤ -2

I want to isolate the x. So I first "move" the 10 to the right side by subtracting 10 from both sides:

-3x ≤ -12

Now I have to get rid of the factor -3 so I have to divide both sides by -3. Since I am dividing by a negative, I have to flip the ≤ into a ≥:

x ≥ 4


You can solve your problem the same way.
Stephen La Rocque.

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