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Question 161518: I have a worksheet and have two questions for you. I am totally lost.
1. Solve 3+2(1-x)>6 or 2x+14< or eual to 8. Graph the solution set on a number line. For this one one of the solutions I came up with is x < or equal to 11. Not sure on the other one.
2. Solve 3+ absolute value 2y-1 absolute value > or equal to 1. Graph the solution set on a number line.
Please help..
Thanks
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i solve first one as follows:
3 + 2*(1-x) > 6
removing parentheses
3 + 2 - 2*x > 6
adding 2*x to both sides and subtracting 6 from both sides gets
3 + 2 - 6 > 2*x
which becomes
5 - 6 > 2*x
which becomes
-1 > 2*x
subtracting 2*x from both sides and adding 1 to both sides and the equation becomes
-2*x > 1
multiplying both sides by -1 and the equation becomes
2*x < -1 (note reversal of inequality.
dividing both sides by 2 and equation becomes
x < -1/2
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i solve second one as follows.
2*x + 14 <= 8
subtracting 14 from both sides and it becomes
2*x <= 8 - 14
which becomes
2*x <= -6
dividing both sides by 2 and it becomes
x <= -3
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third one is a little confusing but i'll assume you mean
3 + |2*y-1| >= 1
subtracting 3 from both sides and the equation becomes
|2*y-1| >= -2
which doesn't make a lot of sense because the absolute value of anything will always be greater than 0, let alone -2.
i can't really solve this part because i don't understand the question very well.
resubmit this one if i got it wrong.
if i got it right, then
|2*y-1| >= -2
is your answer and it will be valid for any value of y and the lowest value of |2*y-1| will be 0.
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back to the first two.
we have 2 equations.
first one is
x < -1/2
second one is
x <= -3
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i don't know if i can draw a number line good enough, but here's an attempt.
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-3 -1/2 0 1/2 3
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x is to the left up to but not including -1/2 for the first equation.
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-3 -1/2 0 1/2 3
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x is to the left up to and including -3 for the second equation.
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