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Solving linear equations and linear inequalities — Basic example

Watch Sal work through a basic Solving linear equations problem.

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  • blobby green style avatar for user Kylie Crawford
    Why did he add 6 to both sides of the equation?
    (57 votes)
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  • hopper cool style avatar for user Nik Unwala
    How do I add 6 to both sides to get the answer? Wouldn't that just completely change the problem?
    (9 votes)
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  • blobby green style avatar for user Aastha Bhandari
    Is practising SAT only from Khan Academy sufficient? I scored 1170 without practising anything in my first full test of SAT, is this a good score for beginner?
    (12 votes)
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    • duskpin sapling style avatar for user Lin Gh.
      I think 1170 is not bad for a first test, but it also depends on how much you want to study. You can also use help from other sites which contain SAT tips that aren't on Khan Academy. I used Khan Academy and prepscholar blog when studying the SAT and ended up in 1400s.
      (31 votes)
  • blobby green style avatar for user Marissa
    my problem with this is that i don't understand why you are doing the steps you are, you need to go more in depth because just telling the steps without explaining why i need to do that step, wont help me remember to do that.
    (10 votes)
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    • primosaur ultimate style avatar for user HumanCalc7
      I'll try and explain why he took the steps he did:
      First of all, the equation is that 3 times l, minus 6, is greater than or equal to 8. The goal is to isolate l and find what it must be greater than or equal to while still keeping the equation the same by changing things on both sides to make it clear what l is greater than or equal to.

      You've probably heard of PEMDAS, which is the order of operations in what to do in solving multistep problems. First you simplify anything with Parantheses, then Exponents, then Multiplication or Division, and finally Addition or Subtraction.
      In the case of changing both sides of an equation, you do it in the opposite order, aka SADMEP.
      However, when you make a change, you want to change both sides of the equation to keep it the same. For example, 10=10. If you add 3 to one side, then 13=10, and it simply doesn't work that way, so you need to make the same change to the other side as well, so 13=13, because it does.

      Now, in the case of this equation, let's do SADMEP. First is subtraction. There's nothing to subtract, because we want just l on the left side and just a number on the right. If the side containing l had any positive numbers, we would subtract their value, thus turning the left side into 3l+0, eliminating that number that is now a zero from the left side and thus making it 3l. However, the left side is 3l-6, so there are no positive numbers. There is, however, a negative number, giving us the chance to add. We want to get rid of that 6, so we need to add 6, because -6+6 is 0, and no one cares about zeros, so the left side is now just 3l. However, as I said earlier, we need to change on the right what we changed on the left. We added 6 on the left, so we now need to add 6 on the right, which currently contains an 8. 8+6=14, so the equation is now "3l is greater than or equal to 14".

      Now SADMEP has only one thing left to do that will bring us to our answer. Our goal is not to make nothing added to l on the left. It is to make the left side nothing but l, and it's currently 3l. Because of this, we need to divide it by 3. 3l/3=l, but we also need to change the other side: 14 divided by 3 equals 14 thirds, or 14/3. This brings us to the final simplified statement that l is greater than or equal to 14/3.

      I hope that helps!
      (31 votes)
  • female robot amelia style avatar for user amna amna
    hi...i'm from Pakistan .I got 92% in matriculation,and 80% in fsc ...plz tell me how many marks are required in SATs for getting admission in LUMS and UK or USA scholorships…..I want to study on fully funded scholorship ...plz guide me
    (8 votes)
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    • duskpin sapling style avatar for user Lin Gh.
      These info are something you should research by yourself. Try looking for scholarships no the internet and contact the university that interests you for more info. Don't forget to read the information provided in the university's home page. Good luck with your college!
      (16 votes)
  • marcimus pink style avatar for user andreynoso
    Why am i supposed to add 6 to both sides
    (4 votes)
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  • starky seedling style avatar for user mallaknattiel
    when am I supposed to change the inequality sign?
    (5 votes)
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  • blobby green style avatar for user addietussing
    This is great thanks! One clarification- when it has the "greater than or equal to" symbol, you pretty much treat it as an equals sign and continue with the algebra to find the variable? Thx!
    (7 votes)
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  • blobby green style avatar for user Caleb Survance
    Why do we flip the sign when divide/multiply by a negative. Obviously that's what makes the equation maintain the same solution but why is it that that works.
    (4 votes)
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  • blobby green style avatar for user Moon07
    Kindly suggest what type of graphing calculator I should purchase to use for SAT in the future.
    (4 votes)
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Video transcript

- [Instructor] Three l minus six is greater than or equal to eight. Which of the following best describes the solutions to the inequality shown above? So it's three times l minus six is greater than or equal to eight. Well, all of these choices, these are in terms of l. They said l on one side, and is greater than or equal to, actually all of these choices are greater than or equal to something else. So let's see what we can do to get just an l on the left-hand side. So the first thing we might wanna do, is let's get rid of this subtracting of six. And the best way we can do that is we can add six. Let's add six to both sides. This six and this six are going to add to zero. And then we are going to be left with, we're going to be left with three l on the left-hand side is greater than or equal to eight plus six is 14. Now just got an l on the left-hand side. We can divide both sides by three. And if you divide both sides by three, you're not going to change the sign. You're not gonna change the inequality. If you're dividing by a negative number you would swap the inequality. Greater than or equal to would turn to less than or equal to. But we're dividing by a positive number, so this is going to be l is greater than or equal to 14 over three. Which is that choice right there.