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Solving Inequalities Using Addition or Subtraction

In this video, we will be learning how to solve inequalities using addition or subtraction.

For Example:

x+7\textless12

x+7-7\textless12-7\leftarrow Subtract 7 from both sides

x\textless5\leftarrow Graph the inequality

xless5

Video-Lesson Transcript

Let’s go over solving inequalities using addition or subtraction.

Solving this is similar to a regular equation except from the inequality sign instead of an equal sign.

For example:

x + 9 \textless 12

Let’s solve for x by subtracting 9 from both sides of the inequality.

x + 9 - 9 \textless 12 - 9

Our answer is

x \textless 3

We can graph this by drawing a number line then encircle the number 3 then draw a line to the left which represents the numbers less than 3.

Now, let’s take a look at subtraction.

We have

x - 7 \textgreater 3

To solve x, let’s just add 7 on both sides.

x - 7 + 7 \textgreater 3 + 7 x \textgreater 10

Now, let’s graph it by drawing a numbe line.

Let’s draw an open circle on 10 and draw a line to the right to represent numbers greater than 10.

If we change the sign of x - 7 \textgreater 3 into x - 7 \geq 3, then our answer would be x \geq 10.

Our graph will have a solid circle on 10 instead of an open circle. Then the line is still going to the right to represent numbers greater than 10.