SOLUTION: given the following inequality: -4(x-3)+5< or equal to 3x-7 a. find solution set for x b. verify answer by checking one value inside the solutions set,and one value outsi

Algebra ->  Equations -> SOLUTION: given the following inequality: -4(x-3)+5< or equal to 3x-7 a. find solution set for x b. verify answer by checking one value inside the solutions set,and one value outsi      Log On


   



Question 117580: given the following inequality: -4(x-3)+5< or equal to 3x-7
a. find solution set for x
b. verify answer by checking one value inside the solutions set,and one value outside the solution set.
c. How does the answer change in the above equation if we change the < or equal to a =
Thank you

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
-4%28x-3%29+%2B+5+%3C=+3x+-+7
-4x+%2B12+%2B+5+%3C=+3x+-+7
-4x+%2B+17+%3C=+3x+-+7
add -17 both sides
-4x+%3C=+3x+-+24
add -3x both sides
-7x+%3C=+-24
multiply both sides by -1 and reverse <
7x+%3E=+24
x+%3E=+24%2F7 answer
check answer
Does x+=+24%2F7 solve original problem?
-4%28x-3%29+%2B+5+%3C=+3x+-+7
-4%28%2824%2F7%29-3%29+%2B+5+%3C=+3%2824%2F7%29+-+7
-%2896%2F7%29+%2B+17+%3C=+%2872%2F7%29+-+7
add -%2872%2F7%29 to both sides
-%28168%2F7%29+%2B+17+%3C=+-7
-%28168%2F7%29+%3C=+-24
-24+%3C=+-24
OK
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What if x+%3E+24%2F7?
Make x+=+25%2F7
-4%28x-3%29+%2B+5+%3C=+3x+-+7
-4%28%2825%2F7%29-3%29+%2B+5+%3C=+3%2825%2F7%29+-+7
-%28100%2F7%29+%2B+17+%3C=+%2875%2F7%29+-+7
-%28175%2F7%29+%3C=+-24
multiply by -7 and change < to > both sides
175+%3E=+168
OK
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Now try a value outside solution set
Make x+=+23%2F7
-4%28x-3%29+%2B+5+%3C=+3x+-+7
-4%28%2823%2F7%29-3%29+%2B+5+%3C=+3%2823%2F7%29+-+7
-%2892%2F7%29+%2B+17+%3C=+%2869%2F7%29+-+7
-%28161%2F7%29+%2B+17+%3C=+-7
-%28161%2F7%29+%3C=+-24
161%2F7+%3E=+24
161+%3E=+168 Not true, x+=+23%2F7 does not solve
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What if we change < to >?
-4%28x-3%29+%2B+5+%3E=+3x+-+7
-4x+%2B+12+%2B+5+%3E=+3x+-+7
-7x+%2B+17+%3E=+-7
-7x+%3E=+-24
7x+%3C=+24
x+%3C=+24%2F7 The > in answer becomes <