Taunja S. answered • 05/09/13

Experienced Tutoring Queen Making Learning Easy

**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 Rule: When 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