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.

2|3x - 2| = 14

Accepted Answer

Welcome back. I'm so glad you're here. We've got this equation five times the absolute value of four, x minus one equals 125. And we are to solve for X when we've got an absolute value bracket in there, what we want to do first is isolate the absolute value on one side of the equation. So let's bring that five over to the other side will divide both sides by five. That leaves us with the absolute value of four, X -1 equals 25. Great. That's how we want it to look. And when we have the absolute value on one side of the equal side, we want to pause and ask ourselves is what's on the other side of the equal side? Greater than or equal to zero? And yes, 25 is greater than or equal to zero, which is great because the absolute value must equal a non negative number, it has to be greater than or equal to zero. So now we can proceed. And the next thing we want to ask ourselves is well what is absolute value? So absolute value tells us the distance that a value in this case for x minus one is from zero on the number line And for X -1 is 25 units away from zero. But it's 25 units away from zero in the positive and in the negative. So what we can do to get rid of those absolute value rackets is set four x minus one equal to negative 25 4 X minus one equal to positive 25. And now we're going to solve for X for both of those equations. This first one we'll add one to both sides. So we've got four X equals negative, 24 will divide both sides by four and negative 24 divided by four gives us X equals negative six. That's one of our answers. And now we'll solve for the other one. We've got to add one to both sides. Again they'll be very similar. Then we've got four X equals and here's the difference 25 plus one is 26 And then we'll divide both sides by four and we get X equals 26 4th. While we can simplify that they're both divisible by two. So X equals 13 halves. We look at our answer choices and that matches with answer choice C. Well done. We'll catch you on the next one.

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