Sure, let’s solve the equation step-by-step.
We start with the given equation:
[tex]\[ y + 6 = -3y + 26 \][/tex]
1. Combine like terms on one side:
First, we want to get all terms involving [tex]\( y \)[/tex] on one side of the equation and constant terms on the other side. To do this, add [tex]\( 3y \)[/tex] to both sides of the equation:
[tex]\[ y + 6 + 3y = -3y + 3y + 26 \][/tex]
[tex]\[ 4y + 6 = 26 \][/tex]
2. Isolate the term with [tex]\( y \)[/tex]:
To solve for [tex]\( y \)[/tex], we need to isolate the variable term. Subtract 6 from both sides of the equation:
[tex]\[ 4y + 6 - 6 = 26 - 6 \][/tex]
[tex]\[ 4y = 20 \][/tex]
3. Solve for [tex]\( y \)[/tex]:
Divide both sides of the equation by 4 to solve for [tex]\( y \)[/tex]:
[tex]\[ \frac{4y}{4} = \frac{20}{4} \][/tex]
[tex]\[ y = 5 \][/tex]
So the solution to the equation [tex]\( y + 6 = -3y + 26 \)[/tex] is:
[tex]\[ y = 5 \][/tex]
Hence, the correct answer is:
[tex]\[ y = 5 \][/tex]
