2 years ago

Which method represents a correct way to solve the inequality 4-2x<6

1 answer:

4 0

First subtract 4 from btoh sides of the equation
4 - 4 - 2x < 6-4
-2x < 2
Now divide both sides by -2
x > -1

NOTE: when dividing by a negative as above the inequality sign is flipped.

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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3x%7D%7Bx%20%7B%7D%5E%7B2%7D%20-%203x%20-%2010%20%7D%20%20-%20%20%5Cfrac%7B6x%7D%

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$\bf \cfrac{3x}{x^2-3x-10}-\cfrac{6x}{x^2-7x+10}\implies \cfrac{3x}{(x-5)(x+2)}-\cfrac{6x}{(x-5)(x-2)}
\\\\\\
\textit{our LCD is clearly then }(x-5)(x+2)(x-2)
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\cfrac{(x-2)3x~~-~~[(x+2)6x]}{(x-5)(x+2)(x-2)}\implies \cfrac{3x^2-6x~~-~~[6x^2+12x]}{(x-5)(x+2)(x-2)}
\\\\\\
\cfrac{3x^2-6x-6x^2-12x}{(x-5)(x+2)(x-2)}\implies \cfrac{-3x^2-18x}{(x-5)(x+2)(x-2)}$