SOLUTION: what is 2k-6 greater than 3k+2 equal to?

Question 672628: what is 2k-6 greater than 3k+2 equal to?

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Given
(1) 2k - 6 > 3k + 2
Solve this the same way you would if it was an equation, but follow the properties of ineqaulities.
First step is to subtract 2k from each side and get
(2) 2k - 2k - 6 > 3k - 2k + 2 or
(3) -6 > k + 2
Now subtract 2 from each side and get
(4) -6 -2 > k + 2 - 2 or
(5) -8 > k or
(6) k < -8
Let try a couple values k to see if we are correct.
First let k = -8, then (1) become
(7) -16 -6 > -24 +2 or
(8) -22 > -22, which is not true.
Let try k = -9, then (1) becomes
(9) -18 - 6 > -27 +2 or
(10) -24 > -25, which is true
So k has to be LESS than -8 to satisfy the given inequality of (1). Just to be sure try k = -7, in (1) and get
(11) -14 -6 > -21 + 2 or
(12) -20 > -19, which is false (not true)
Answer: k < -8
Note: Neither of the arithmetic operations of subtraction in the above steps "violate" the properties (rules) of inequalities.
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