Solve each equation or inequality. |6 - 2x | + 1 = 3

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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 minus three X plus three is equal to eight. So in this case we're looking for the value of X. Which means we want to isolate X and X is inside the absolute value. So we want to think about what the absolute value is doing to the values inside of it. So inside the absolute value we could have a positive 5 -3 x Plus three is equal to eight. But we could also have a negative 5 -3 x. And we could have a negative five minus three X. Because recall that the absolute value makes a negative number positive. So that means that the values inside the absolute value could still be negative. So in order to find all the solutions for X we want to consider both of these scenarios. So I'm going to start by solving if five minus three X was positive. So in this case I can combine five and three to give me negative three X plus eight is equal to eight. And to find a solution for X. I need to isolate X. Also tracked eight from both sides leaving me with negative three X is equal to eight minus eight is zero. So when I divide by negative three to isolate X. I have X is equal to zero. So that's if the components inside of the absolute value were positive. Now we can see if they were negative. So I have this negative one that I need to distribute, so negative one times five is negative five negative one times negative three X is positive three X. And I still have the plus three equal to eight. And I can combine the negative five and the positive three. So it gives me three X. Negative five. Plus three is negative two equal to eight and I'll add two to both sides in order to start isolating X. Leaving me with three X is equal to 10. And finally I'll divide by three. That gives me X. Is equal to 13th. So you can see that because of the absolute value, I actually have two solutions for X. So X could be zero or it could be 10 divided by three. So this becomes my final solutions for X. And this equation. And you can see that answer choice C. Also has zero and 13th. So hopefully this video helped and see you next time.

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Solve each equation or inequality. |6 - 2x | + 1 = 3

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