Solve each equation. | x - 4/ 2| = 5

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Hello everyone. In this video, we're going to be looking at this practice problem where we want to solve for x and the equation, absolute value of X -5 divided by three is equal to six. So in this case, we're working with an absolute value. So we want to think about what the absolute value is doing to the components inside of it. So recall that an absolute value could have a positive number inside. So it could be positive X - Divided by three is equal to six. But an absolute value could also have a negative number inside. So it would be negative X -5 divided by three is equal to six. And recall that it could be negative because an absolute value converts the negative or a negative number inside of it into a positive answer. So say for example, I had the absolute value of positive two, I would get back to. But if I have the absolute value of -2, I also get back to. So even though these twos had opposite signs, they output ID the same result. So this is why when we're solving for X and an absolute value, we have to consider both of these scenarios because although the output may be the same, we could have a negative X or a negative value of that X. So we have to consider both of these options. And I'll start by solving this positive Value and I'll do that by multiplying by three. So I have X -5 because the three's cancel out is equal to six times three, which is 18. In order to isolate X, I'll add five to both sides. So that leaves me with X is equal to 23. And now we need to do the same for if the inside of that suit value was negative. So I'll deal with this negative first, I'll divide by negative one on both sides. So that cancels out the negative, that leaves me with X -5 divided by three is equal to negative six. And once again, all multiplied by three. So the three's cancel out on the left hand side and I'm left with X -5 is equal to negative 18, add five to both sides and isolate X. So now I have X is equal to negative 18 plus five which is negative 13. And from here, you can see that X has two solutions, I could be X could be -13 or positive 23. And you can see that these two solutions arose because of the absolute value. So when we are working with an absolute value. You have to consider both of those scenarios for the inside. It could be positive or a negative number. If we look at the answer choices, you can see that answer choice D also has negative 13 and positive 23. So hopefully this video helped and see you next time.

Solve each equation. | x - 4/ 2| = 5

Key Concepts

Absolute Value

Linear Equations

Case Analysis

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