absolute value inequalities

absolute value of x+3=7
x+3=7           x+3= -7
x=10              x= -4

When you have an absolute value, you have to make an equation set to an even number and another equation set to an odd number.  When you have an absolute value, most of the time you end up with two different answers.  For this equation we have the absolute value of x+3=7.  To solve this, you have to make two separate equations which are x+3=7 and x+3= -7.  Then you just solve for x after and get x=10 and x= -4.

absolute value of 3x-9 is greater than or equal to 9
3x-9 is greater than or equal to 9                     3x-9 is less than or equal to -9
3x greater or equal 18                                       3x less or equal 0
x greater or equal 6                                             x less or equal 0

For this one you aren't given an equal sign, but you solve the same way.  For this problem you set each to a postive and negative 9. The only extra step you have to do is for the negative 9 you have to switch the sign and that makes it less than or equal too.  Then you solve the problem, but you cant forget if you divide by a negative number you have to reverse the sign also.  So when we solve this problem, we get x greater or equal to 6 and x lessor equal to 0.