Solve each equation. |3x - 1 | = 2

Question

Accepted Answer

Hello everyone. In this video, we're going to be looking at this practice problem where we want to sell for X in the equation, absolute value of two X minus five is equal to seven. So in this case, you can see that the X is inside an absolute value. So we want to think about what the absolute value is doing to the components inside of it. So we take the absolute value of a number, let's say take the absolute value of a number eight, we get back that same number A. But if we take the absolute value of a negative number such as negative A, we also get back eight. So you can see that the absolute value only affected the negative number because it got rid of the negative sign. So when we're solving for X inside the absolute value, we have to consider the situation where we could be getting the same output. But in reality, the inside has different signs. So we're gonna use this to help us find the solutions for X. So because X is inside the absolute value, we said that this could truly be positive two X - is equal to seven. But it could also be -2, X -5 is equal to seven because the absolute value would cancel out that negative or mask of that negative and turn the output to be positive. But we still need to consider it since X is inside that absolute value. So if I solve for X, if the inside was positive, I'll add five to both sides leaving you with two, X is equal to seven plus five, just 12 and to completely isolate X, I'll divide by two on both sides. So it leaves me with X is equal to 12, divided by two, which is six. And now we need to solve if the inside was negative, I'll start by distributing this negative. So I have negative one times two, X is negative two, X negative one times negative five is positive five, still equal to seven. And now I'll start by subtracting five from both sides. So it leaves me with negative two. X is equal to positive two because seven minus five is two and to completely isolate X all divided by negative two. So it leaves me with X is equal to negative one. So now you can see that I have two solutions for X because of the absolute value. So because of the absolute value X could be equal to negative one or positive six. So this becomes my final solution for X. And if we look at the answer choices, you can see that answer choice c also has a negative one and positive six. So hopefully this video helped and see you next time.

Solve each equation. |3x - 1 | = 2

Key Concepts

Absolute Value

Linear Equations

Case Analysis

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