To solve the equation [tex]\(6y - 20 = 2y - 4\)[/tex], follow these steps:
1. Isolate the variable [tex]\(y\)[/tex] on one side of the equation:
Start by subtracting [tex]\(2y\)[/tex] from both sides to get all [tex]\(y\)[/tex] terms on one side.
[tex]\[
6y - 20 - 2y = 2y - 4 - 2y
\][/tex]
Simplifying this gives:
[tex]\[
4y - 20 = -4
\][/tex]
2. Solve for [tex]\(y\)[/tex]:
Next, add 20 to both sides to isolate the term with [tex]\(y\)[/tex].
[tex]\[
4y - 20 + 20 = -4 + 20
\][/tex]
Simplifying this, we get:
[tex]\[
4y = 16
\][/tex]
3. Divide both sides by 4:
To solve for [tex]\(y\)[/tex], divide both sides by 4.
[tex]\[
y = \frac{16}{4}
\][/tex]
Simplifying this, we get:
[tex]\[
y = 4
\][/tex]
4. Check your solution:
Substitute [tex]\(y = 4\)[/tex] back into the original equation to verify it satisfies both sides.
[tex]\[
6(4) - 20 = 2(4) - 4
\][/tex]
Simplifying:
[tex]\[
24 - 20 = 8 - 4
\][/tex]
[tex]\[
4 = 4
\][/tex]
Since both sides of the equation are equal, our solution is correct.
Thus, the value of [tex]\(y\)[/tex] that satisfies the equation [tex]\(6y - 20 = 2y - 4\)[/tex] is [tex]\(y = 4\)[/tex].
The best answer is [tex]\( \boxed{y = 4} \)[/tex].
