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-5x >15 how do i solve this

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2 Answers

Hi Karlee,

Inequalities are a lot like regular equations except when there is an equal sign and you have x raised to the first power, there is one solution. You are going to find a set of numbers that will satisfy the inequality.

Since an inequality is an equation, we can use all of the same rules we use to move stuff from side to side of an equation with an equal sign with the exception of multiplying by -1. So, let's get x by itself.

First, divide through by 5 and move it to the right.

-x > 3

Second step: multiply through by -1. This reverses the inequality.

x < -3

x is a label for the real number line. This inequality says I want all x that are less than -3. On the real number line, this corresponds to all numbers to the left of -3. And since we do NOT have an equal sign, we CANNOT include -3 itself. 

So, we draw a line representing the real number line and we label a few numbers to the left and right of -3. We then draw a thick line starting at -3 extending to the left; this represents our solution. Now, we have to indicate that -3 is NOT part of the solution. One way of doing this is by putting an empty circle at -3 and starting the line at the circle. 

-5x > 15

-5x/-5 < 15/-5    (divide both sides by -5, this changes the inequality to >)

x < -3

 

The graph will be a vertical dotted line (because of the < ) at x = -3.  Shading will be to the left of the line.