If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra (all content)>Unit 2

Lesson 15: Two-step inequalities

# Two-step inequalities

Two-step inequalities are slightly more complicated than one-step inequalities (duh!). This is a worked example of solving ⅔>-4y-8⅓. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• why is it so hard to learn?
• because it helps our brains grow and keeps us on top of becoming smarter.
• How would you then answer a question like this type?
4x − 3/2− 3x − 3/3< 3
I cant find any references to this type of equation, since i don't think it is a multi-step inequality
• a calculator would probably help
• I was trying to solve a multi-step inequality but I don't know how to. The inequality is:
-1/4(8n-12) ≥ −2n−1 When I try to solve it the n variable no longer exists and I don't understand how I would continue to solve. When I looked online they said the answer would be all real numbers are solutions but I still do not understand. Please help.
• 1) Distribute the -1/4 on the left side
-1/4(8n-12) ≥ −2n−1
-2n+3 ≥ −2n−1
2) Add 2n to both sides
3 ≥ −1
So, as you have found already, the variable disappears. The inequality that remains is True. 3 is greater than -1. This is called an identify. It tells us that any value of "n" that you use in the inequality will be a solution. So, the solution is all real numbers. You can see this for yourself by picking any value you like for "n" and checking to see if it is a solution. All values will work.

Here are a couple of other scenarios that you might run into:
If your inequality had become 3 ≥ 3, this is also true (an identity). So, again the solution is all real numbers.

If your inequality becomes something like 3 < 1, this is False ( 3 is never less than 1). This is called a contradiction. It means that the inequality has no solution.
• does it matter which side the variable terms are
• If you mean "Does it matter-left or right side of the equals sign?" then no.
However, it is important to get the variable on one side, either the left or the right.
• This is harder than rocket science!
• Actually, if you can solve a 2-step equation, you can solve 2-step inequalities. The same techniques are used. The only thing that is different is that if you multiply/divide the inequality by a negative value, then you reverse the inequality.

And, by the way, multi-step inequalities and many more advanced math topics are used in rocket science. So, a 2-step inequality is not harder than rocket science.
• Why do you have to swap the inequality so that it is less than?
• *When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side!* This is why you must flip the sign whenever you multiply by a negative number.
• Where did you get the 25/3 from?
• Sal converted the mixed number 8 1/3 to an improper fraction which is equal to 25/3. Hope this helped!
• At Sal divides -12y by -12 but when I divided by a negative number in the problem: 16x -7 < or = -71 (I divided - -64 by -16) the answer was wrong. I don't understand why it was wrong, please explain why.
-- Did you reverse the inequality since you divided by a negative?
-- How did you get 2 "-" in front of the 64? -71+7 = -64
-- Did you finish the math? -64/(-16) = 4

So the final result should be: x >= 4

Hope this helps.
Note: If this if in a practice problem, use the Hints to figure out what you did incorrect. This allows you to learn from your mistake(s).