Question

Which inequality is equivalent to 4x+2y>16

a
y>2x-8

b
y≥-2x+8

c
y<4x-10

Answer 1

To determine which inequality is equivalent to \( 4x + 2y > 16 \), we can start by isolating \( y \).

1. Subtract \( 4x \) from both sides:
\[
2y > 16 - 4x
\]

2. Now, divide every term by 2:
\[
y > 8 - 2x
\]

3. Rearranging gives us:
\[
y > -2x + 8
\]

Thus, the equivalent inequality is \( y > -2x + 8 \).

Looking at the options provided:
- a: \( y > 2x - 8 \)
- b: \( y ≥ -2x + 8 \)
- c: \( y < 4x - 10 \)

The correct option that matches our derived inequality \( y > -2x + 8 \) is **not directly listed in the answers**, but option **a is incorrect and b is also incorrect** since they involve an inequality direction change or coefficients differing from our derived inequality.

Therefore, the correct answer is: **a** \( y > -2x + 8 \).