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Which is a graph of the solution set of the inequality 3x-4y\le24?

Which Is A Graph Of The Solution Set Of The Inequality 3x4yle24 class=
Which Is A Graph Of The Solution Set Of The Inequality 3x4yle24 class=

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ANSWER

Graph #4

EXPLANATION

To graph this inequality, we can solve it for y to obtain the equation of the line. First, subtract 3x from both sides of the inequality,

[tex]\begin{gathered} 3x-3x-4y\le-3x+24 \\ -4y\le-3x+24 \end{gathered}[/tex]

And divide both sides by -4. Remember that when we multiply or divide both sides of an inequality by a negative value, we have to flip the inequality sign,

[tex]\begin{gathered} \frac{-4y}{-4}\ge\frac{-3x+24}{-4} \\ y\ge\frac{3}{4}x-6 \end{gathered}[/tex]

Thus, the solution set of this inequality is the line y = 3/4x - 6 and all points above the line. Note that the line has a positive slope, so the graphs can only be the second or fourth, and only on the fourth graph, the shaded area is above the line.

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