To fix an inequality that includes only one variable, simply follow the same measures you offered to solve equations. In other words, simplify both political parties of the inequality, isolation the variable, and then get rid of the variable"s coefficient. However, over there is one major difference between equations and also inequalities: as soon as solving one inequality, if you ever multiply or division both political parties by a an adverse number, you need to reverse the inequality sign.

You are watching: When do you reverse the inequality sign

What execute I typical by "reverse" the inequality sign? readjust less than indications to greater than signs, and also vice versa. (Less than or same to signs end up being greater than or equal to signs, and vice versa.) I call this the inequality the atmosphere swing. Remember, it only happens once you multiply or divide by a an unfavorable number, and also that just occurs once you"re make the efforts to remove the coefficient. So, just remember to check for a an adverse coefficient together you"re removed it, and reverse the inequality authorize as necessary.

Critical Point

When you solved equations, you were advised to carry out the very same things to both political parties of the same sign. Follow the same procedures now, but do whatever to both sides of the inequality authorize instead.

Example 2: deal with the inequality -5x + 3 > -32.

Solution: due to the fact that both sides are currently simplified (no sides contain prefer terms), isolate the change by individually 3 ~ above both political parties of the higher than sign. An alert that the inequality authorize does not change yet, due to the fact that you"re not multiplying or separating by a an adverse number.

-5x > -35

Time to eliminate the coefficient. Perform so by splitting both political parties by -5. Don"t forget to turning back the inequality sign because you"re splitting by a an unfavorable number.


So, any kind of number less than 7, once plugged in because that x, need to make this inequality explain true. Girlfriend obviously can"t examine them every to make sure your answer is appropriate (you"d invest the remainder of her life check your occupational on one problem), yet it doesn"t ache to check one answer just to make certain you"re not means off. Here"s just how you could inspect the value x = 6, which should work, because it"s less than 7:

-5(6) + 3 > -32-30 + 3 > -32-27 > -32

Since 32 is larger than 27, climate -32 is definitely less than -27, for this reason x = 6 is a precious answer.

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Excerpted indigenous The finish Idiot"s overview to Algebra 2004 by W. Michael Kelley. All civil liberties reserved consisting of the appropriate of reproduction in totality or in component in any type of form. Supplied by setup with Alpha Books, a member the Penguin group (USA) Inc.