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How do you solve Multi-Step Inequalties?

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Multi-Step Inequalities can seem very intimidating but once you know the rules it's not as hard as you think.  Multi-Step Inequalities can be solved the same as any Multi-Step Equation. 

Here is an example for how to solve a multi-step inequality:   

                                          2x + 7 > 49

                               Goal is to get x by itself. Find out what x is greater than and/or equal to.

  Step #1: To find out what x is you must eliminate the extra numbers on the side of the variable. Use Inverse (Opposite) Operation to accomplish this.

                                          2x + 7 > 49 

  Subtract 7 from both sides.       2x +7 > 49

                                                           -7      -7

                     Then you have         2x > 42

Use Inverse Operation again by dividing 2 from both sides to get x by itself.

                     So then you have    2x/2 > 42/2

                   Your Answer is:            x > 21  (Any # that is 21 or above is x)

 

Now let's say you have                 -2x + 7 > 49

Rules change when you have negative integers (numbers) and you have to multiply or divide by them then you change the direction of your inequality symbol.

 

     So let's see here

                                                    -2x +7 > 49        

     Use Inverse Operation by subtracting 7 from both sides. 

                                                   -2x +7 > 49

                                                          -7     -7

         Now you have:                   -2x  >  42

Use Inverse Operation by dividing -2 from both sides.

  Special RuleWhen you multiply or divide by a negative number, SWITCH Your Sign.

                                                    -2x/-2  >  49/-2

                      Your Answer:           x  <  -21   (x is equal to or less than -21)

 

Christian I hope that these examples help you to better understand how to solve multi-step inequalities.  Please let me know if you need more examples.  If you need help with multiplying or dividing integers I have an easy tip for that as well.  Looking forward to hearing from you.

Thank for the opportunity to be of assistance to you.

Taunja Smith, WyzAnt Tutoring Queen