SOLUTION: PLEASE HELP: 2 | x-2 | greater than or equal to 3 thankyou~

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.

RELATED QUESTIONS
PLEASE HELP: 2 | x-2 | greater than or equal to 3... (answered by jim_thompson5910)

Please Help me find all the subsets of D={x/-2≤x<3, x is an integer}... (answered by stanbon)

Can I please have help with this, thank you! Graph the following systems of... (answered by Alan3354,ikleyn)

PLEASE ANSWER ALL OF THESE i help 3. 2x-y>4 ; (-6,-15) 5. 5x+2y less than or... (answered by JBarnum)

please help 4/5x + 2 greater or equal to 2/5 and 1-6x less than or equal to... (answered by ankor@dixie-net.com)

Please help me graph this inequalitie on rectangular coordinate system. y is equal to or (answered by stanbon)

Please help and explain: x^3-4x greater than or equal to 0 (answered by josgarithmetic,DrBeeee,tommyt3rd)

the compound inequality x<-2 or x greater than or equal to 3 using interval notation (answered by fractalier)

f(x)={-x if x greater or equal to 3} 2 if x is greater than 3... (answered by solver91311)