In Exercises 91–100, find all values of x satisfying the given co...

Question

In Exercises 91–100, find all values of x satisfying the given conditions.

y = |2 - 3x| and y = 13

Accepted Answer

Welcome back. I'm so glad you're here. We've got this equation, we have Y equals the absolute value of 13 minus two X. And we are to solve for X. Were also given that Y equals one. So we can go ahead and substitute in one for that Y. So now it's one equals the absolute value of 13 minus two X. And we always want to pause when we have absolute value by itself on one side of the equation and ask ourselves is the thing on the other side of the equation in this case are one, Is that greater than or equal to zero? And yes it is. Which is great because it means we can proceed if it were a negative number, we would have an answer of no solution. But since it's positive in this case we can go on. Our next question is we want to ask ourselves what is absolute value anyway. Well the absolute value is the distance something is from zero. So in this case it's the distance that 13 minus two X is from zero and that is one unit away from zero but it's not only one unit in the positive direction, it's one unit in the negative direction as well. So 13 minus two X equals negative one and positive one. And that's how we're going to go ahead and solve for X. We set 13 minus two, X equal to negative one and 13 minus two X equal to positive one. And now we just go ahead and solve for X. So let's subtract 13 from both sides. So now we have a negative two. X equals a negative 14. We'll divide both sides by negative two and that will leave us with X equals while negative 14 divided by negative two is seven. There's one of our solutions for X and now for the other one, we're going to subtract 13 from both sides again. And that will give us a negative two. X equals in this time a negative 12, divide both sides by a negative two, and that will give us X equals negative 12 divided by negative two is a positive six are two solutions for the absolute value equation are six and seven, which makes sense. We should have two solutions when we're dealing with absolute value, we look at our answer choices and that matches answer choice. A well done. We'll catch you on the next one.

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