Algebra 1
posted by Anonymous .
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 )
 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