Our actual answer that we got, 3 times 3 minus 9 has got But if we divide the left sideīy 3, we have to divide the right side by 3.

Times x divided by 3 is just going to be x. Just left with 3x, and on the right-hand side, you are Get rid of the negative 9 on the left-hand side, we add 9 toīoth sides of the equation. So solving this equation isįairly straightforward.

If you had, say, a 1 here, youĬould say, oh well, then this thing could be a 1 The 0 is that, it's the only number the has a unique, So if I told you that theĪbsolute value of 3x minus 9 is 0, than we know that 3x minusĩ has to be equal to 0, and that's kind of unique about That's the only value whoseĪbsolute value is 0. Value of x is equal to 0, you know that x has That something has to be exactly 0 away from 0, or 0 awayįrom the origin on the number line. Value of something is equal to 0, I'm telling you So we're told that theĪbsolute value of the something- in this case the So let's just rewrite theĪbsolute value equation. Value of 3x minus 9 is equal to 0, and graph the solution We didn't need to think about the two different possibilities of the stuff inside the absolute value signs, because we knew that it had to be equal to 0. When you do this method of accounting for case 1 and then case 2, you usually find that you get two different answers.īut for THIS problem, we didn't need to do any of that, because the problem was equal to 0, which means that the stuff inside the absolute value sign also had to be equal to 0. So you get rid of the absolute value signs and change the sign of everything inside the absolute value, and then you solve the whole problem a second time. Therefore, the absolute value symbols changed the sign of the stuff inside of them, which is the same thing as changing their signs. In the second case, you assume that the stuff inside the absolute value signs was negative, and taking the absolute value of it made it positive. Then, once you've finished doing the problem that way, you have to come back and solve the second case.

In the first case, you assume that the stuff inside the parentheses is already a positive number, so you can just get rid of the absolute value signs and solve the problem as though they aren't even there. The equation Sal was solving was |3x-9|=0, right? Well, normally, you solve equations with an absolute value in them by considering two cases. I think the reason that the method is a little bit different here than what you are used to is because in this particular problem there was a 0 on the right hand side of the equation.

Khan academy absolute value