Solve each equation

Question

|x-5|=|-2x+6|

Answer 1

1, Assuming both arguments are positive

x - 5 = -2x + 6

2x - 5 = 6

2x = 11

x = 5.5

2. Assuming both arguments are negative

-(x - 5) = -(-2x + 6)

x - 5 = -2x + 6

x = 5.5

3. Assuming the first positive, second negative

x - 5 = -(-2x + 6)

x - 5 = 2x - 6

-5 = x - 6

1 = x

4. Assuming the first negative, second positive

-(x - 5) = -2x + 6

-x + 5 = -2x + 6

x = 1

 

{1, 5}