How do you solve a linear inequality 3x + 2y < 6?

Jul 20, 2018

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color(red)(y<(6-3x)/2

Explanation:

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We are given the inequality: color(blue)(3x+2y<6

$\Rightarrow 3 x + 2 y < 6$

Subtract color(red)(3x from both sides of the inequality.

$\Rightarrow 3 x + 2 y - 3 x < 6 - 3 x$

$\Rightarrow \cancel{3 x} + 2 y - \cancel{3 x} < 6 - 3 x$

$\Rightarrow 2 y < 6 - 3 x$

Divide both sides of the inequality by color(red)(2

$\Rightarrow \frac{2 y}{2} < \frac{6 - 3 x}{2}$

$\Rightarrow \frac{\cancel{2} y}{\cancel{2}} < \frac{6 - 3 x}{2}$

$\Rightarrow y < \frac{6 - 3 x}{2}$

Hence, our final solution is given by:

color(blue)(y<(6-3x)/2

We can also graph this solution as given below:

Note that the dotted line in the graph indicates value that is NOT a part of the final solution.

Hope this helps.