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Question 233186: I need help solving this problem
-5≤2x+5 and 2x+5<9
The solution is {X|██≤X<██}
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! -5≤2x+5 and 2x+5<9
This is equivalent to:
-5 <= 2x+5 < 9
whatever you do to one side of the equation, you have to do to all the other sides.
subtract 5 from all sides of the equation to get:
-5 -5 <= 2x + 5 - 5 < 9 - 5
this becomes:
-10 <= 2x < 4
divide all sides of this equation by 2 to get:
-5 <= x < 2
test in the original equation to see if the original equation holds true.
take several values of x within the limits and outside of the limits.
try x = -6, -5, 0, 1, 2
-6 and 2 are outside the limits. -5, 0, 1 are within the limits.
when x = -6, equation of -5 <= 2x+5 < 9 becomes:
-5 <= -12 + 5 < 9 which becomes:
-5 <= -7 < 9 which is NOT true because -5 is NOT <= -7
this is ok because -6 was outside the limits.
when x = -5, equation of -5 <= 2x+5 < 9 becomes:
-5 <= -10 + 5 < 9 which becomes:
-5 <= -5 < 9 which IS true.
this is ok because -5 was within the limits.
when x = 0, equation of -5 <= 2x+5 < 9 becomes:
-5 <= 0 + 5 <= 9 which becomes:
-5 <= 0 <= 9 which IS true.
this is ok because 0 was within the limits.
when x = 1, equation of -5 <= 2x+5 < 9 becomes:
-5 <= 2 + 5 < 9 which becomes:
-5 <= 7 < 9 which IS true.
this is ok because 1 was within the limits.
when x = 2, equation of -5 <= 2x+5 < 9 becomes:
-5 <= 4 + 5 < 9 which becomes:
-5 <= 9 < 9 which is NOT true because 9 is not < 9.
this is ok because 2 was outside the limits.
equation looks good and your answer is:
-5 <= x < 2
which is the same as:
-5 <= x and x < 2.
this is also the same as:
x >= -5 and x < 2
you could also have done each of the inequalities separately and then combined them.
your equation was:
-5 <= 2x + 5 and 2x+5 < 9
solve -5 <= 2x + 5 to get -5 <= x
solve 2x + 5 < 9 to get x < 2
-5 <= x and x < 2 is equivalent to -5 <= x < 9.
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