To solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] given the equation [tex]\( 4x + \frac{1}{2}y = 3 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
4x + \frac{1}{2}y = 3
\][/tex]
2. Isolate the term with [tex]\( y \)[/tex] on one side of the equation. Subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[
\frac{1}{2}y = 3 - 4x
\][/tex]
3. Solve for [tex]\( y \)[/tex] by multiplying both sides of the equation by 2 to get rid of the fraction:
[tex]\[
y = 2(3 - 4x)
\][/tex]
4. Simplify the expression:
[tex]\[
y = 6 - 8x
\][/tex]
Now that we have [tex]\( y = 6 - 8x \)[/tex], we can compare this result to the given options:
- Option A: [tex]\( y = (4x + 3) \times 2 \)[/tex]
[tex]\[
y = 2(4x + 3) = 8x + 6
\][/tex]
This does not match [tex]\( y = 6 - 8x \)[/tex].
- Option B: [tex]\( y = 2(-4x + 3) \)[/tex]
[tex]\[
y = 2(-4x + 3) = -8x + 6
\][/tex]
This also does not match [tex]\( y = 6 - 8x \)[/tex].
- Option C: [tex]\( y = (-4x + 3) \div 2 \)[/tex]
[tex]\[
y = \frac{-4x + 3}{2} = -2x + 1.5
\][/tex]
This does not match [tex]\( y = 6 - 8x \)[/tex] either.
- Option D: [tex]\( y = 8x - 6 \)[/tex]
This does not match [tex]\( y = 6 - 8x \)[/tex] either.
None of the options directly matches [tex]\( y = 6 - 8x \)[/tex], hence there seems to be no correct option provided in the choices.
