To solve an inequality that contains only one variable, just follow the same steps you offered to deal with equations. In other words, simplify both sides of the inequality, isolate the variable, and then get rid of the variable"s coefficient. However, there is one major difference in between equations and also inequalities: when solving one inequality, if you ever multiply or divide both political parties by a an adverse number, you have to reverse the inequality sign.

You are watching: When to switch the inequality sign

What execute I mean by "reverse" the inequality sign? adjust less than indications to better than signs, and also vice versa. (Less than or same to signs come to be greater 보다 or equal to signs, and also vice versa.) I speak to this the inequality the atmosphere swing. Remember, it just happens once you multiply or division by a negative number, and that just occurs when you"re do the efforts to remove the coefficient. So, just remember to check for a an unfavorable coefficient together you"re removed it, and also reverse the inequality authorize as necessary.

Critical Point

When you resolved equations, you were advised to do the very same things come both political parties of the equal sign. Follow the same actions now, yet do every little thing to both political parties of the inequality authorize instead.

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

Solution: since both sides are currently simplified (no sides contain like terms), isolation the variable by subtracting 3 top top both political parties of the greater than sign. Notification that the inequality sign does not readjust yet, since you"re no multiplying or splitting by a an adverse number.

-5x > -35

Time to eliminate the coefficient. Do so by separating both sides by -5. Don"t forget to turning back the inequality sign due to the fact that you"re dividing by a negative number.


So, any number much less than 7, as soon as plugged in because that x, have to make this inequality explain true. You obviously can"t examine them every to make sure your price is appropriate (you"d spend the remainder of your life check your work on one problem), however it doesn"t hurt to check one answer just to make sure you"re not means off. Here"s how you could check the value x = 6, which have to work, because it"s much less than 7:

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

Since 32 is bigger than 27, climate -32 is certainly less than -27, therefore x = 6 is a valid answer.

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Excerpted native The complete Idiot"s overview to Algebra 2004 through W. Michael Kelley. All civil liberties reserved including the ideal of reproduction in entirety or in component in any form. Supplied by plan with Alpha Books, a member the Penguin group (USA) Inc.