What does it mean to slove for inequality?

[Stouffville]

 

[Dr.Peterson]

What does it mean to slove for inequality?​

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The phrase is not to "solve for an inequality", but to solve an inequality for a variable. What it means is to find the values of the variable (here, x) for which the inequality is true. Usually the answer will be a simpler inequality, something like [imath]x > 5[/imath], or a compound inequality like [imath]0\le x\le 9\text{ or } x\ge 12[/imath]. (Those are not the answers to these!)

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There is a standard method for solving these, which I would assume you have been taught (though you probably haven't learned it yet). If you don't have a textbook that explains this, you might read something like this:

Solving Rational Inequalities

A Rational Expression looks like ... Sometimes we need to solve rational inequalities like these

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Of course, this problem tells you to solve by graphing, not by the algebraic methods taught there (which you'll presumably get to soon); but that shows what the graphs can look like. There are more examples here:

2.4: Solution of Rational Inequalities by Graphing

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