Question
Solve the following inequality for \( y \). \[ 4 x-2 y \leq 8 \]
Ask by Gibson Salazar. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y \leq -4 + 2x \)
Solution
Solve the equation \( 4x-2y=8 \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(4x-2y=8\)
- step1: Move the expression to the right side:
\(-2y=8-4x\)
- step2: Change the signs:
\(2y=-8+4x\)
- step3: Divide both sides:
\(\frac{2y}{2}=\frac{-8+4x}{2}\)
- step4: Divide the numbers:
\(y=-4+2x\)
The solution to the inequality \(4x-2y \leq 8\) is \(y \leq -4+2x\).
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Simplify this solution Beyond the Answer
To solve the inequality \( 4x - 2y \leq 8 \) for \( y \), we start by isolating \( y \): 1. Subtract \( 4x \) from both sides: \[ -2y \leq 8 - 4x \] 2. Now, divide each term by \(-2\). Remember, when dividing by a negative number, we must flip the inequality sign: \[ y \geq -4 + 2x \] So, the solution to the inequality is: \[ y \geq 2x - 4 \] This describes a region above the line \( y = 2x - 4 \) in the Cartesian plane.
