Solve for x: | -2x + 3 | = | x - 15 |?

Question

6, -6

6, -12

-6, 12

-6 only

Answer 1

-2x+3=x-15  or  -2x+3=-(x-15)

3x=18          or  -2x+3=-x+15

x=6              or  x=-12

answer is B 6 and -12

Answer 2

6, -6

always absolute value last, just pretend there perentice's

Answer 3

You need to define ranges for x in which it would be solved.

The ranges would be based on values of x where (-2x+3) = 0 and (x-15) = 0, i.e. x = 1.5 and x = 15

a) for x < 1.5,

(-2x+3) > 0 which means |-2x+3| = (-2x+3)

(x-15) < 0 which means|x-15| = -(x-15) = 15-x

Thus, in this range we solve:

-2x+3 = 15-x

=> x = -12

b) for 1.5 < x < 15,

(-2x+3) < 0 which means |-2x+3| = -(-2x+3) = 2x -3

(x-15) < 0 which means|x-15| = -(x-15) = 15-x

Thus, in this range we solve:

2x-3 = 15-x

=> 3x = 18

=> x = 6

c) for x > 15

(-2x+3) < 0 which means |-2x+3| = -(-2x+3) = 2x -3

(x-15) > 0 which means|x-15| = (x-15)

Thus, in this range we solve:

2x-3 = x-15

=> x = -12

But since, the range is for x >15, this solution is invalid.

So, the answers are: x = -12 and x = 6