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.

$x + 9 - 9 \textless 12 - 9$

$x \textless 3$

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 $10$.