What is

x = 1

Step-by-step explanation:

Given

- | x + 2 | + 1 = 4x - 6 ( subtract 1 from both sides )

- | x + 2 | = 4x - 7 ( multiply both sides by - 1 )

| x + 2 | = - 4x + 7

The absolute value always returns a positive value, but the expression inside can be positive or negative, thus

x + 2 = - 4x + 7 ( add 4x to both sides )

5x + 2 = 7 ( subtract 2 from both sides )

5x = 5 ( divide both sides by 5 )

x = 1

OR

- (x + 2) = - 4x + 7, that is

- x - 2 = - 4x + 7 ( add 4x to both sides )

3x - 2 = 7 ( add 2 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

As a check substitute these values into both sides of the equation and if both sides are equal then they are the solutions.

x = 1 : - |1 + 2| + 1 = - | 3 | + 1 = - 3 + 1 = - 2

right side = 4(1) - 6 = 4 - 6 = - 2 ← True

x = 3 : - |3 + 2| + 1 = - |5| + 1 = - 5 + 1 = - 4

right side = 4(3) - 6 = 12 - 6 = 6 ← False

Thus x = 3 is an extraneous solution and

x = 1 is the solution

Step-by-step explanation:

right

step-by-step explanation: