The Secret to Solving Two Step Inequalities

Here’s how to Solve Two Step Inequalities

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The Short Answer to “What are Two Step Inequalities?”

Two Step Inequalities will be inequalities that need two steps to simplify. You have to add, subtract, multiply, or divide multiple times to simplify the inequality. When simplifying every Two Step Inequality you should either add or subtract first and after that multiply or divide second. You can tell when an expression is an inequality by checking the symbol in the middle of the expression. If the symbol is a greater than, greater than or equal to, less than, or less than or equal to symbol then the expression is an inequality. In the event that you multiply or divide by a negative number, the inequality sign changes directions. The inequality sign will change when answering how to solve inequalities for any kind of inequality symbol.

3 Easy Steps for solving any Two Step Inequalities Example

1. Add or subtract the constant to get just the variable on one side of the inequality.
2. Multiply or divide so that you cancel out the coefficient on the term.
3. If you have to multiply or divide by a negative number then the inequality symbol changes directions.

 

Two Step Inequalities Practice Problems Quiz

Watch the video explanation of our Two Step Inequalities Worksheet

Watch our free video on how to solve Two Step Inequalities. This video shows how to solve problems that are on our free solving two step inequalities worksheet that you can get by submitting your email above.

Watch the free Two Step Inequalities video on YouTube here: Two Step Inequalities Video

Video Transcript:

This video is about solving 2 step inequalities. You can get the two-step inequalities worksheet with answers used in this video for free by clicking on the link in the description below. In order to solve two step inequalities, you follow rules that are very similar to solving two step equations. The main difference being that instead of an equal sign in the middle of your equation, or inequality, you have one of four types of inequality symbols. The first thing to solving inequalities is that you solve it just like you would for an equation and that you solve for the variable. You’re still going to try to isolate the variable on one side of the inequality. The second thing you must remember about inequalities and what makes it a little bit different than solving for equations is that if you multiply or divide by a negative you have to flip the sign of your inequality symbol. The only time you do this is when you multiply or divide by a negative number.

Now we’re going to do a real quick example of solving a two step inequality. In this example we have 3x minus 25 is less than 35. We’re going to draw our line down the middle of our inequality. We know that we have to isolate this x by getting it on one side of the inequality by itself. The first thing we need to do is we need to get rid of this minus 25. We’re going to add 25 to both sides. This 25 will cancel. We bring down the 3x, our less than sign in the middle, and then 35 plus 25 is 60. Then this is like saying 3 times x  the opposite of 3 times something is to divide by 3.  we’re going to divide both sides by 3 and on this side we have x. Then we have our less than sign in the middle and then 60 divided by 3 is 20. You can see this is very similar to solving for equations except we have an inequality sign in the middle of our inequality. And if you divide by a negative or multiply by a negative number you will flip that sign in the middle. Let’s do a couple practice problems on our two step inequalities worksheet.

The first thing we’re going to do on our two step inequalities practice worksheet is number one. This problem gives us 9x minus 9 is greater than 9. We know we have to isolate the x and get the x by itself on one side of the inequality. In order to do that we have this minus 9 which is the first thing we have to get rid of. We’re going to add 9 to both sides because the opposite of minus 9 is plus 9. These will cancel on the left side and we have 9x. Then in the middle we still have greater than and then 9 plus 9 is 18. Now 9x is greater than 18 is what our inequality states. This is like saying 9 times x and the opposite of 9 times x is to divide by 9. That will cancel whatever you do to this side you also have to do this side. We’re going to divide by 9 on this side. Now we have x on the left the greater than symbol in the middle and then 18 divided by 9 on the right which is equal to 2. Our final solution is x is greater than 2.

Jumping down to number three on our two step inequalities worksheet we have negative 10x plus 14 is greater than or equal to 134. Again we’re going to follow the same steps that we just did or like just like you do when you’re solving for two step equations. The first thing we need to do is get rid of this plus 14, so we’re trying to get this x by itself. We have to get rid of this plus 14 so we subtract 14 here so that it cancels and then whatever you do on one side you also have to do the other. We subtract 14 here on this side. We have negative 10x is greater than or equal to in the middle and then 134 minus 14 is 120. Then the next step is to get rid of this negative 10 that’s being multiplied times the x. The opposite of that is to divide by negative 10 so that the tens cancel and the negatives cancel and then whatever you do to one side you do the other. We divide this side by negative 10. Now what is different about inequalities is that because we just divided by a negative number, we have to flip the sign in the middle. This greater than or equal to turns into a less than or equal to symbol, so it switches. It’s different it’s changed then you just solve. 120 divided by negative 1 is negative 12. Our answer is x is less than or equal to negative 12.

The last problem we’re going to do on our two step inequalities worksheet is number seven. This problem gives us negative x minus eight is less than 31. Again we’re going to draw our line down the middle to get this x by itself on one side. We’re going to add 8 so that the 8 will cancel. Whatever due to one side you do the other. We bring down our negative x our symbol in the middle, is less than, and then 31 plus 8 is 39. Now this negative x is like saying negative 1, even though it’s not written, times x. We have to get rid of this negative 1 by dividing by negative 1.  We divide this side by negative 1. Now we have x and remember we divided by a negative so the symbol in the middle has to change. Our less than symbol becomes a greater than symbol and then 39 divided by negative 1 is negative 39 and that’s our solution. Hopefully you found this article and video helpful when learning how to solve 2 step inequalities.