Question

Solve the equation 5+7 | 2x-1 | = -44

Answer 1

The easy part is isolating the absolute-value term:

5 + 7 |2x - 1| = -44

7 |2x - 1| = -49

|2x - 1| = -7

Remember that the absolute value function returns a positive number that you can think of as the "size" of that number, or the positive distance between that number and zero. If x is a positive number, its absolute value is the same number, |x| = x. But if x is negative, then the absolute value returns its negative, |x| = -x, which makes it positive. (If x = 0, you can use either result, since -0 is still 0.)

The important thing to take from this is that there are 2 cases to consider: is the expression in the absolute value positive, or is it negative?

• If 2x - 1 > 0, then |2x - 1| = 2x - 1. Then the equation becomes

2x - 1 = -7

2x = -6

x = -3

• If 2x - 1 < 0, then |2x - 1| = - (2x - 1) = 1 - 2x. Then

1 - 2x = -7

-2x = -8

x = 4