To solve the equation [tex]\(6y - 20 = 2y - 4\)[/tex], we need to perform a series of algebraic steps to isolate [tex]\(y\)[/tex]. Follow these steps:
1. Move all terms involving [tex]\(y\)[/tex] to one side of the equation and constant terms to the other side:
[tex]\[
6y - 20 = 2y - 4
\][/tex]
Subtract [tex]\(2y\)[/tex] from both sides to combine the [tex]\(y\)[/tex] terms:
[tex]\[
6y - 2y - 20 = -4
\][/tex]
This simplifies to:
[tex]\[
4y - 20 = -4
\][/tex]
2. Move the constant term on the left side to the right side of the equation:
Add 20 to both sides to isolate the [tex]\(y\)[/tex] term:
[tex]\[
4y - 20 + 20 = -4 + 20
\][/tex]
This simplifies to:
[tex]\[
4y = 16
\][/tex]
3. Solve for [tex]\(y\)[/tex]:
Divide both sides by 4 to find [tex]\(y\)[/tex]:
[tex]\[
y = \frac{16}{4}
\][/tex]
[tex]\[
y = 4
\][/tex]
The value of [tex]\(y\)[/tex] that satisfies the equation [tex]\(6y - 20 = 2y - 4\)[/tex] is [tex]\(y = 4\)[/tex]. Therefore, the correct answer is:
D. [tex]\(y = 4\)[/tex]
