Solve each equation. Rewrite the equation as two cases.

Question

1). The absolute value of x - 2 minus 3 equals 5.

A: I know one of the solutions is 10. However, I do not believe there is a second solution.

2). The absolute value of x + 7 increased by 2 = 10.

A: I know one of the solutions is 1. However, I am uncertain of what the other is.

Answer 1

1 )

| x - 2 | - 3 = 5 Add 3 to both sides

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

| x - 2 | = 8

x - 2 = + OR - 8

First solution :

x - 2 = 8 Add 2 to both sides

x - 2 + 2 = 8 + 2

x = 10

Second solution :

x - 2 = - 8 Add 2 to both sides

x - 2 + 2 = - 8 + 2

x = - 6

Solutions :

x = - 6 and x = 10

2 )

| x + 7 | + 2 = 10 Subtract 2 to both sides

| x + 7 | + 2 - 2 = 10 - 2

| x + 7 | = 8

x + 7 = + OR - 8

First solution :

x + 7 = 8 Subtract 7 to both sides

x + 7 - 7 = 8 - 7

x = 1

Second solution :

x + 7 = - 8 Subtract 7 to both sides

x + 7 - 7 = - 8 - 7

x = - 15

Solutions :

x = 1 and x = - 15