Question 664087
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.