Learn How To Solve Inequalities Using Addition Or Subtraction

In this video, we will be learning how to solve inequalities using addition or subtraction. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

Example of Solving an Inequality with Addition/Subtraction

$x+7\textless12$

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

$x\textless5\leftarrow$ Graph the inequality

Example 1

$x+9\textless10$

Subtract $9$ from both sides

$x+9-9\textless10-9$

$x\textless1$

Now, graph the inequality

Example 2

$x-4\geq2$

Add $4$ from both sides

$x-4+4\geq2+4$

$x\geq6$

Now, graph the inequality

Video-Lesson Transcript

Let’s go over how to solve inequalities using addition or subtraction.

Solving this is similar to a regular equation except for 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 $10$ .

Solving Inequalities Using Addition or Subtraction

Example of Solving an Inequality with Addition/Subtraction

Example 1

Example 2

Video-Lesson Transcript