Solve the equation. Check for extraneous solutions.

2|7-7x|=2x+4

2|7 - 7x| = 2x + 4

|7 - 7x| = x + 2

7 - 7x = x + 2 or 7 - 7x = - (x + 2)

-8x = - 5 or 7 - 7x = - x - 2

x = 5/8 or - 6x = - 9

x = 5/8 or x = 9/6

x = 5/8 or x = 3/2

To check for extraneous solutions, we check both solutions in the original equation.

Check solution 5/8:

2|7 - 7x| = 2x + 4

|7 - 7x| = x + 2

|7 - 7 * 5/8| = 5/8 + 2

|56/8 - 35/8| = 5/8 + 16/8

21/8 = 21/8

Solution x = 5/8 works.

Check solution 3/2:

2|7 - 7x| = 2x + 4

|7 - 7x| = x + 2

|7 - 7 * 3/2| = 3/2 + 2

|14/2 - 21/2| = 3/2 + 4/2

|-7/2| = 7/2

7/2 = 7/2

Solution 3/2 also works.

Answer: x = 5/8 or x = 3/2