To solve the equation [tex]\(14x - 7y = 21\)[/tex] for [tex]\(y\)[/tex], follow these steps:
1. Isolate the term containing [tex]\(y\)[/tex]: Start by isolating the term [tex]\( -7y \)[/tex] on one side of the equation.
[tex]\[
14x - 7y = 21
\][/tex]
2. Subtract [tex]\(14x\)[/tex] from both sides: To move [tex]\(14x\)[/tex] to the other side of the equation, subtract it from both sides.
[tex]\[
-7y = 21 - 14x
\][/tex]
3. Rearrange the equation: Notice that we can rewrite the right side for clarity, but it remains untouched by the mathematical operation.
[tex]\[
-7y = -14x + 21
\][/tex]
4. Divide by [tex]\(-7\)[/tex]: To solve for [tex]\(y\)[/tex], divide every term on both sides of the equation by [tex]\(-7\)[/tex].
[tex]\[
y = \frac{-14x + 21}{-7}
\][/tex]
5. Simplify the fraction: Simplify each term inside the fraction separately.
[tex]\[
y = \frac{-14x}{-7} + \frac{21}{-7}
\][/tex]
[tex]\[
y = 2x - 3
\][/tex]
So, the solution is:
[tex]\[
y = 2x - 3
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{2x - 3} \)[/tex], corresponding to option [tex]\( \text{A.} \ y = 2x - 3 \)[/tex].
