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\( \begin{array}{ll}\text { Match the graph } & \text { a. } y<-3 \\ \text { with its inequality. } & \text { b. } x \geq 2 \\ & \text { c. } 5 x+10 y>0 \\ & \text { d. } y9 \\ & \text { g. } 3 y-4 x \geq 12 \\ \text { h. } y \leq-2 x-4 \\ \text { i. } 8 x-6 y<10 \\ \text { j. } 3 x-1 \geq y\end{array} \)

Ask by Peters Wang. in the United States
Feb 03,2025

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a. \( y < -3 \) b. \( x \geq 2 \) c. \( 5x + 10y > 0 \) d. \( y < x \) e. \( 2y - x \leq 6 \) f. \( 6x + 3y > 9 \) g. \( 3y - 4x \geq 12 \) h. \( y \leq -2x - 4 \) i. \( 8x - 6y < 10 \) j. \( 3x - 1 \geq y \)

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Bonus Knowledge

The graphs associated with each inequality can reveal fascinating aspects of how equations transform into visual representations! For instance, the inequality \(y < -3\) corresponds to a horizontal line at \(y = -3\) where all points below this line satisfy the inequality—such an area paints a simple but striking visual! On the flip side, if you dive into \(5x + 10y > 0\), you can start to envision a line that separates the plane into regions of solutions and non-solutions. This line can be simplified to \(y > -\frac{1}{2}x\), and everything above it is part of the solution set. Splendid, right? Graphs are like a visual escape room—only instead of keys, you’re unlocking solutions!

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