Find the number:

Question

Twice the difference of a number and three is four more than the number.

Answer 1

2*abs(x-3) = x + 4

Case 1: x > 3

2*(x-3) = x + 4

2x - 6 = x = 4

x = 10

Case 2: x < 3

2*(3-x) = x + 4

6 - 2x = x + 4

2 = 3x

2/3 = x

Check: x = 10

2*abs(x-3) = x + 4

2*abs(10 - 3) = 10 + 4

2*(7) = 14

14 = 14 OK

Check: x = 2/3

2*abs(x-3) = x + 4

2*abs[ (2/3 - 3 ] = 2/3 + 4

2*abs[ 2/3 - 9/3 ] = 2/3 + 12/3

2*(7/3) = 14/3

14/3 = 14/3 OK

2 Solutions: x = 10, 2/3

Answer 2

the difference of a number and three: (x-3)

twice that: 2(x-3)

four more than the number: x+4

equate them: 2(x-3) = x+4

Now solve: 2x-6 = x+4

2x-x = 4+6

x = 10