Solve each equation. |3/ 2x - 1 | = 4

Question

Accepted Answer

Hello everyone. In this video, we're going to be looking at this practice problem where we want to solve for X in the equation, absolute value of five divided by three X minus two is equal to six. So in this case, you can see that we're working with an absolute value. So we want to consider how the absolute value is affecting our equation. So recall that when I take the absolute value of number such as A, I get back A but if I take the absolute value of a number that is negative such as negative A, I also get back A. So notice how these equations have different inputs with the only difference being the sign the top is positive and the bottom is negative but the outputs are the same. So because the outputs are the same on these equations, we have to consider that an absolute value could be hiding a negative. So this absolute value could be five divided by three X -2, It's equal to six, But it could also be negative five divided by three X -2 is equal to six because a negative inside of the absolute value appears to have the same output as a positive number. So we have to consider both of these scenarios when we're solving for X. So if I begin to solve for X, if the inside was positive, I'll multiply by three X minus two on both sides. So that cancels out the three X -2 in the denominator on the left hand side. So that leaves me with five is equal to six times three, X is 18 X six times negative two is negative 12. In order to isolate X, I'll add 12 to both sides. So that leaves me with 17 is equal to 18 X and I'll divide by 18 to fully isolate X salt is made with X is equal to positive 17/18, you can see X is completely isolated. So now I'll look at if the inside of the absolute value was negative And I'll distribute the negative to this five and I'll do the same multiplication of three X -2 to get the x out of the denominator. So three X minus two cancels on the left hand side, leaving me with negative five is equal to six times three, X is 18 X, six times negative two is negative 12. I'll add 12 to both sides. So that leaves me with seven is equal to 18 X. And again, I'll divide by 18 to completely isolate X leaves me with X is equal to seven divided by 18. So you can see that when I solved it, considering that the inside was negative, I get a different answer. So that means because of the absolute value X actually has two values, it could be seven divided by 18, could be 17, divided by 18. So these become my final answer for this problem. And you can see that answer. Choice eight also has positive seven divided by 18 and positive 17 divided by 18. So hopefully this video helped and see you next time.

Solve each equation. |3/ 2x - 1 | = 4

Key Concepts

Absolute Value

Linear Equations

Isolating the Variable

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