# Solving One-Step Inequalities

Hello! Welcome to this video on solving one-step inequalities. This process should look very similar to the process of solving one-step equations.

Let’s jump into some examples!

$$x+7\gt -3$$

Since the goal, like with solving equations, is to isolate $$x$$ on one side, we need to get rid of the $$+7$$ on the left side. We do this by subtracting 7 from both sides, just like with a one-step equation.

$$x+7-7\gt -3-7$$

$$x\gt -10$$

And this is our answer for our inequality. Sometimes when you have one-step inequalities you’ll be asked to graph your solution. So if you were to graph this solution, it would look something like this:

Since we have a greater than sign, and not greater than or equal to, $$–10$$ is not in the solution set. We show this with an open circle above $$–10$$.

Let’s try another one! Solve the inequality:

$$x-\leq 23$$

To isolate $$x$$ on the right side, add 2 to both sides.

$$x-2+2\leq 3+2$$

$$x\leq 5$$

Now let’s draw a graph of our solution. Because there is a less than or equal to sign, 5 is included in our answer, and we use a closed dot on our graph.

Now let’s try an example where we have to use division.

$$-4x\geq 16$$

To isolate $$x$$, we will have to divide both sides by $$–4$$.

$$\frac{-4x}{-4}\geq \frac{16}{-4}$$

However, before we go forward, I need to tell you of one special rule. When we divide or multiply by a negative number with inequalities, we have to flip our inequality sign. If you don’t, your answer will be wrong. So here, our answer will be:

$$x\leq -4$$

It’s very important that you flip your inequality sign when multiplying or dividing by a negative number. Now let’s graph our answer. Since we have a less than or equal to sign again, we use a closed dot.

Let’s work through one more example together.

$$\frac{x}{6}\lt 1$$

To isolate $$x$$, we need to multiply both sides by 6.

$$6\cdot \frac{x}{6}\leq 16$$

$$x\lt 6$$

Because we multiplied by a positive number, we don’t have to flip our inequality sign. Then we can graph our solution. We’re gonna draw an open circle above 6 because we have a less than sign, 6 is not included in the solution set.

I hope this video on solving one-step inequalities was helpful. Thanks for watching, and happy studying!