Absolute Value Equation

[nycmath]

Solve for x.

| 3x + 8 | + 5 = 2

Begin by isolating the absolute value. To do so, subtract 5 from both sides.

| 3x + 8 | + 5 - 5 = 2 - 5

| 3x + 8 | + 0 = -3

| 3x + 8 | = -3

Absolute value will never equal a negative value.

The number -3 tells us to stop right here. No need to create two cases.

The answer is DNE or empty set.

Try one.

Solve for x.

| 6x + 7 | - 10 = -15