Question 664087: PLEASE HELP:
2 | x-2 | greater than or equal to 3
thankyou~
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 2 * |x-2| >= 3
if (x-2) is positive, then the equation becomes:
2 * (x-2) >= 3
simplify to get:
2x - 4 >= 3
add 4 to both sides to get 2x >= 7
divide both sides by 2 to get x >= 7/2
if (x-2) is negative, then the equation becomes:
2 * -(x-2) >= 3
simplify to get:
-2x + 4 >= 3
subtract 4 from both sides to get -2x >= -1
divide both sides by -2 to get x <= 1/2
your solutions are:
x >= 7/2
x <= 1/2
put these solutions in your original equation to see if the equation holds true.
original equation is:
2 * |x-2| >= 3
when x = 7/2, equation becomes 2 * |7/2-2| >= 3
simplify to get 2 * |3/2| >= 3
simplify to get 6/2 >= 3 which becomes 3 >= 3 which is true
you should also test for x > 7/2.
pick a nice clean number like 8 and go through the drill and you should see that the equation is still true.
when x = 1/2, equation becomes 2 * |1/2 - 2| >= 3
simplify to get 2 * |-3/2| >= 3
simplify to get 2 * 3/2 >= 3 which becomes 3 >= 3 which is true.
you should also test for x < 1/2.
pick a nice clean number like 0 and go through the drill and you should see that the equation is still true.
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