Question
Solve the following inequality for \( y \). \( \begin{array}{l}4 x-2 y \leq 8\end{array} \)
Ask by Ray Riley. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y \geq 2x - 4 \)
Solution
We start with the inequality:
4x - 2y ≤ 8
Step 1: Isolate the term containing y by subtracting 4x from both sides:
-2y ≤ 8 - 4x
Step 2: Divide both sides by -2. Remember, when you divide an inequality by a negative number, you must reverse the inequality sign:
y ≥ (8 - 4x) / (-2)
Step 3: Simplify the right-hand side:
y ≥ -4 + 2x
Thus, the solution to the inequality is:
y ≥ 2x - 4
This means that for any value of x, y must be greater than or equal to 2x - 4.
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Simplify this solution The Deep Dive
To solve the inequality \( 4x - 2y \leq 8 \) for \( y \), you can isolate \( y \) on one side of the inequality. Start by rearranging the inequality: 1. Subtract \( 4x \) from both sides: \(-2y \leq 8 - 4x\) 2. Now divide the entire inequality by \(-2\). Remember that when you divide or multiply by a negative number, you must flip the inequality sign: \( y \geq 2x - 4\) So, the solution for \( y \) in terms of \( x \) is: \( y \geq 2x - 4 \).
