Question
Solve the following inequality for \( y \). \( -3 x+4 y \leq 12 \)
Ask by Reid Griffin. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y \leq \frac{12 + 3x}{4} \)
Solution
Solve the equation \( -3x+4y=12 \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(-3x+4y=12\)
- step1: Move the expression to the right side:
\(4y=12+3x\)
- step2: Divide both sides:
\(\frac{4y}{4}=\frac{12+3x}{4}\)
- step3: Divide the numbers:
\(y=\frac{12+3x}{4}\)
The solution to the inequality \( -3x+4y \leq 12 \) is \( y \leq \frac{12+3x}{4} \).
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Simplify this solution Bonus Knowledge
To solve the inequality \( -3x + 4y \leq 12 \) for \( y \), first isolate \( y \). Start by adding \( 3x \) to both sides: \[ 4y \leq 3x + 12 \] Next, divide every term by 4 to solve for \( y \): \[ y \leq \frac{3}{4}x + 3 \] This gives you the solution in terms of \( y \). The line \( y = \frac{3}{4}x + 3 \) represents the boundary, and since it's a "less than or equal to" inequality, the area below this line (including the line itself) represents the solutions to the inequality.
