SOLUTION: abs is indicated by ; ;3-5x; -2 is > or = 0 I'd like help as soon as possible.

Question 612810: abs is indicated by ;
;3-5x; -2 is > or = 0
I'd like help as soon as possible.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
abs is usually indicated by | which is the shift version of the backslash key.
the backslash key is equal to \ which is usually right above the enter key depending on which keyboard you are using.

if i understood it correctly, your problem is:
|3-5x| - 2 >= 0
add 2 to both sides of the equation to get:
|3-5x| >= 2
if the expression within the absolute value symbols is positive, then the equation becomes:
3-5x >= 2
subtract 3 from both sides of the equation to get:
-5x >= -1
divide both sides of the equation by -1/5 to get:
x <= 1/5
don't forget that multiplying both sides of an inequality by a negative number reverses the inequality.
if the expression within the absolute value symbols is negative, then the equation becomes:
-(3-5x) >= 2
simplify this by removing parentheses to get:
-3+5x >= 2
add 3 to both sides of the equation to get:
5x >= 5
divide both sides of the equation by 5 to get:
x >= 1
multiplying both sides of an inequality by a positve number does not reverse the inequality.
your answer is that x is either <= 1/5 or >= 1.
this equation can be graphed as 2 equations.
the first equation is y = abs(3-5x) which is an equivalent equation to y = |3-5x|.
the second equation is y = 2.
the solution to the graph is the values of x when the value of y in the equation of y = abs(3-5x) is greater than the value of y in the equation of y = 2.
the graph is shown below:

looking at the graph, you can see that this occurs when x is <= 1/5 and when x is >= 1.
the alternative to the graph is to plug value in for x in both equations to see where the value of y lies.
when x = 1/5, abs(3-5x) = 3 - 1 = 2
when x = 1, abs(3-5x) = abs(3-5) = abs(-2) = 2
when x = 0 (smaller than 1/5), abs(3-5x) = abs(3) = 3 which is > 2.
when x = 2 (greater than 1), abs(3-5x) = abs(3-10) = abs(-7) = 7 which is > 2.
your solution is x <= 1/5 or x >= 1.

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