Solve for x: |2x + 6| − 4 = 20

Question

just need to solve for x.

Answer 1

The equation is |2x+6| - 4 = 20 .

First rewrite the above equation in the form |ax+b| = c where c = 20 ≥0 and it is equivalent to the statement  ax+b = c or ax+b = - c.

Add 4 to each side.

|2x+6| - 4+4  = 20+4

|2x+6|  = 24.

Rewrite the equation |2x+6|  = 24 as two equations .

2x+6  = 24 or 2x+6  = -24 Then solve each equation separately.

Solve the equation 1: 2x+6  = 24

Subtract 6 from each side.

2x+6 -6 = 24-6

2x = 18

Divide each side by 2.

2x/2 = 18/2

x = 18/2

x = 9.

Solve the equation 2: 2x+6  = -24.

Subtract  6 from each side.

2x+6 -6 = -24-6

2x = -30

Divide each side by 2.

2x/2  = -30/2

x  = -30/2

x = -15.

The solutions of the equation are  9 and -15.

Answer 2

The equation is |2x+6| - 4 = 20.

Add 4 to each side.

|2x+6| - 4+4  = 20+4

|2x+6|  = 24.

Write the above equation in the form |ax+b| = c where c = 24 ≥0 and it is equivalent to the statement  ax+b = c or ax+b = - c.

Rewrite the equation |2x+6|  = 24 as two equations 2x+6  = 24 or 2x+6  = -24.

Then solve each equation separately.

Solve the equation 1: 2x+6  = 24

Subtract 6 from each side.

2x+6 -6 = 24-6

2x = 18

Divide each side by 2.

2x/2 = 18/2

x = 18/2

x = 9.

Solve the equation 2: 2x+6  = -24.

Subtract  6 from each side.

2x+6 -6 = -24-6

2x = -30

Divide each side by 2.

2x/2  = -30/2

x  = -30/2

x = -15.

The solutions of the equation are  9 and -15.