 Hello, this is a video about solving linear equations. The first thing we need to talk about is identifying an equation. An equation contains an equal sign while an algebraic expression does not. An example one will identify each of the following as either an expression or equation. Looking at part A, there is no equal sign, so that means we have an expression. In part B, 4x minus 13 equals 13. There is an equal sign. We do have an equation. In part C, once again we have an equal sign. That means that we have ourselves an equation. A few little things to note about solving linear equations. First off, when we solve linear equations, the goal is to find the solution, a value which makes the equation true. Next, if you see x equals 2 or 2 equals x, they both have the same meaning. Next, as we go through and solve equations, the purpose of an equation is that we have two sides that are equal to each other. So if you add or subtract something from one side of the equation, then you have to add it or subtract it from the other side. If you multiply or divide by something on one side of the equation, then it must be multiplied or divided by on the other side. Some steps to solving linear equations. Step one, we'll clear the fractions. Step two, we'll distribute and remove parentheses. Step three, we'll combine like terms on each side of the equation. Step four, we'll get the variable terms on one side of the equation and constant terms on the other. Step five, we'll simplify and solve. Step six, if you want, you can actually plug in the solutions and check your answer. Now one important thing to note about these steps is that steps one and two can often be interchanged. Some people like to distribute first and then clear the fractions. I am one of those people. Example two, let's solve some linear equations now. In part A, it give me y minus 7 equals negative 6y. You have y's on both sides of the equation, so your goal is to get the variable term on both on one side of the equation. So in this case I have a 1y and it's negative 6y. I'm just going to go ahead and subtract 1y from both sides of the equation, giving me negative 7 equals negative 7y. Your goal is to get y by itself, but you're multiplying by negative 7. You have to undo multiplication, meaning you need to divide both sides by a number. Since you're multiplying by negative 7, divide both sides by negative 7. This gives you 1 equals y, which is the same thing as saying y equals 1. Second equation, in part B you have 9x minus 15 equals 10x plus 3. Once again, variables on both sides of the equation have a 9x on the left, a 9x on the right. I will take away 9x from both sides. This gives me negative 15 equals x plus 3. You're getting x by itself, but there's a plus 3 attached to it. The only way to undo plus 3 is to minus 3 on both sides of the equation. This gives you negative 18 equals x, or x equals negative 18. In part C, we finally have a chance to distribute the 7 to the set of parentheses that follows, 7 times in parentheses x minus 1. This will give us 7x plus 8 equals 7 times x is 7x. 7 times negative 1 is minus 7. We have variable terms on both sides of the equation. There's a 7x on the left, a 7x on the right. The moment you go in and subtract 7x from both sides of the equation, you'll get the following. 8 equals negative 7. Now the variables canceled out in this case, leaving us with 8 equals negative 7, which is totally never true. When you get a statement that's never true, that means the equation actually has no solution. In part D, you have all these fractions with 3s in the denominators. Our goal here is to go through and multiply every single term, or fraction in this case, by 3. Since we're multiplying fractions together, some of you might like to see it written as 3 over 1. 3 times 2 is 6, 1 times 3 is 3, then you have x. Plus 3 times 6 is 18, 1 times 3 is 3, 3 times 4 is 12, and once again, 1 times 3 is 3. Don't forget the negative sign. I have to do a little bit of housekeeping here. 6 over 3 gives me 2x, 18 over 3 gives me 6 equals, 12 over 3 gives me 4, and that's negative. The goal is to get the x term by itself, but there's a plus 6 attached to it. Taking away 6 from both sides, that gives us 2x equals negative 10. You want to get x by itself, but you're multiplying by 2. Divide both sides by 2, you get x equals negative 5. In part E, I can now distribute 3 times x is 3x, 3 times negative 4 is negative 12. We get 3x minus 12 equals 3x minus 12. This seems a little bit weird, but the moment we take away 3x from both sides, we're actually left with negative 12 equals negative 12, which is always true. Once again, this is a special case because the variables are all canceled out, leaving you with negative 12 equals negative 12, but this time we get something that is always true. So the solution for this equation has to be all real numbers. Anything will work. In part F, you have fractions again, so I'm going to go through, since 7 is what's in the denominator, I will multiply through by 7, or 7 over 1. This will give me 7 times 6, which is 42, over 1 times 7, which is 7. Y equals 7 times negative 12, which is negative 84, over 1 times 1, which is 1. Simplifying gives me 6y equals negative 84. We want y by itself, but you're multiplying by 6. Divide both sides by 6 to get y equals negative 14. That's an introduction on how you solve linear equations. Thanks for watching.