To solve the equation:
[tex]\[ 2.8y + 6 + 0.2y = 5y - 14 \][/tex]
we'll follow these steps:
1. Combine like terms on the left side of the equation:
[tex]\[
2.8y + 0.2y + 6 = 5y - 14
\][/tex]
[tex]\[
3y + 6 = 5y - 14
\][/tex]
2. Move the terms involving [tex]\( y \)[/tex] to one side of the equation and the constant terms to the other side:
Subtract [tex]\( 3y \)[/tex] from both sides:
[tex]\[
6 = 5y - 3y - 14
\][/tex]
Simplify:
[tex]\[
6 = 2y - 14
\][/tex]
3. Isolate the term involving [tex]\( y \)[/tex] on one side:
Add 14 to both sides:
[tex]\[
6 + 14 = 2y
\][/tex]
Simplify:
[tex]\[
20 = 2y
\][/tex]
4. Solve for [tex]\( y \)[/tex]:
Divide both sides by 2:
[tex]\[
y = \frac{20}{2}
\][/tex]
[tex]\[
y = 10
\][/tex]
Thus, the solution to the equation [tex]\( 2.8y + 6 + 0.2y = 5y - 14 \)[/tex] is:
[tex]\[
y = 10
\][/tex]
Among the given choices, the correct answer is:
[tex]\[
y = 10
\][/tex]
