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The solution to the inequality \( 3x + 2y > 4 \) is \( y > \frac{4 - 3x}{2} \).
Solución
1. Start with the inequality:
\[
3x + 2y > 4
\]
2. Subtract \( 3x \) from both sides to isolate the term with \( y \):
\[
2y > 4 - 3x
\]
3. Divide both sides by \( 2 \) to solve for \( y \) (note that dividing by a positive number does not change the direction of the inequality):
\[
y > \frac{4 - 3x}{2}
\]
The solution to the inequality is:
\[
y > \frac{4 - 3x}{2}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Bonus Knowledge
To solve \( 3x + 2y > 4 \), let's first rewrite it as an equation \( 3x + 2y = 4 \) to find the boundary line. When you graph this line on a coordinate plane, you'll see that it separates the plane into two half-planes. You'll shade above the line for the inequality \( 3x + 2y > 4 \) since we are looking for values where the left side is greater than 4. Now, a fun tip: Choose a test point that's not on the line (like (0,0)) to determine which side to shade. Substituting (0,0) into the inequality gives \( 0 > 4 \), which is false, so you shade the opposite side. Voila, you've got your solution region!
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