Question
Solve the following inequality for \( y \). \( 4 x-2 y \leq 8 \)
Ask by Mejia Murray. 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 with y:
Subtract 4x from both sides:
-2y ≤ 8 - 4x
Step 2. Divide both sides by -2. Remember, dividing by a negative number reverses the inequality symbol:
y ≥ (8 - 4x) / (-2)
Step 3. Simplify the right-hand side:
(8 - 4x) / (-2) = -8/2 + (4x)/2 = -4 + 2x = 2x - 4
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 \( y \), we first want to isolate \( y \). Start by subtracting \( 4x \) from both sides: \[ -2y \leq 8 - 4x \] Next, divide every term by \(-2\). Remember, when we divide or multiply by a negative number, we must reverse the inequality sign: \[ y \geq \frac{4x - 8}{2} \] Simplifying the right side: \[ y \geq 2x - 4 \] Thus, the solution for the inequality is: \[ y \geq 2x - 4 \]
