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
Solve each equation. Rewrite the equation as two cases.
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.
1 answer