SOLUTION: I need help. When solved for x, the solution set for |7x-3|is greater than or equal to|2x+5| is {x:x greater than or equal to k or x greater than or equal to w}. Find the sum (k+w)

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Question 946809: I need help. When solved for x, the solution set for |7x-3|is greater than or equal to|2x+5| is {x:x greater than or equal to k or x greater than or equal to w}. Find the sum (k+w). Express your answer as a common or improper fraction reduced to lowest terms.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you have abs(7x-3) >= abs(2x+5)

abs(...) is the same as |...| which means absolute value of ...

this can be solved as:

7x-3 >= 2x+5 or 7x-3 <= -(2x+5)

solve for x in 7x-3 >= 2x+5 and you get x >= 8/5.

solve for x in 7x-3 <= -(2x+5) and you get x <= -2/9.

your solution is all values of x such that x <= -2/9 or x >= 8/5

the following graph shows the solution.

the red line is y = abs(7x-3)

the blue line is y = abs(2x+5)

x = .222 is the same as x = -2/9.

x = 1.6 is the same as x = 8/5.

you can see that the y values on the red line are greater than or equal to the y values on the blue line when x is less than or equal to .222 and when x is greater than or equal to 1.6.