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.

|x - 2| = 7

Accepted Answer

Welcome back. I'm so glad you're here. We have this equation, the absolute value of X -5 equals 24. And whenever we have an absolute value on one side of an equal sign, we want to pause and ask ourselves, is the number on the other side of the equal sign greater than or equal to zero. So in this case is 24 greater than or equal to zero and yes, 24 is greater than zero, which that's great. It means we can proceed if that 24 Was a negative number, we would have to stop but now we can go ahead and ask ourselves well what is absolute value anyway, absolute value is the distance that a value is from zero. So this X -5 is 24 units away from zero, but not only 24 units in the positive direction, but it's also 24 units in the negative direction as well. So what we can do next is set X -5 equal to negative 24 and X -5 equal to positive 24. And now we can solve for X, we'll go ahead and add five to both sides. So we get X equals and on the right hand side negative, 24 plus five is negative 19. There's one of our answers. Now we'll again add five to both sides. And on the left hand side we've got X equals and on the right hand side, 24 plus five is 29 those are our two answer choices negative 19 and 29. And that matches answer choice B. Well done, we'll catch you on the next one.

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