In Exercises 61–76, solve each absolute value equation or indicat...

Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution.

|2x - 1| = 5

Accepted Answer

Welcome back. I'm so glad you're here. We've got this absolute value equation. The absolute value of four X minus six equals 14. And what we want to do whenever we have an absolute value all by itself on one side of the equation we want to pause and ask ourselves, is the other side of the equation greater than or equal to zero? So is this 14 greater than or equal to zero? And it is 14 is greater than zero, which is great because that means we can proceed if it's a negative number over there, we can't proceed but in this case we can So what we do next is think to ourselves what is absolute value anyway? Well, absolute value is the distance of value is from zero. So it's the distance that four x minus six is from zero and four X minus six is 14 units away from zero. But not only is it 14 positive units from zero, it's 14 units away from zero in the negative direction as well. So in order to solve for X, we can set four x minus six equal to both negative 14 and positive 14. And now we can solve for X will add six to both sides and that gives us four X equals negative eight, divide both sides by four, and one of our answers is x equals negative two for the other one. It's going to be very similar, adding six to both sides and here's where it's different. We have four X equals 14 plus six is 20 And will divide both sides by four and we have X equals five. We look at our answer choices and this matches answer choice B. Well done. We'll catch you on the next one.

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