Answer :
To solve the equation \( y + 6 = -3y + 26 \), follow these steps:
1. Combine Like Terms:
[tex]\[ y + 6 = -3y + 26 \][/tex]
To isolate the variable \( y \) on one side, add \( 3y \) to both sides:
[tex]\[ y + 3y + 6 = 26 \][/tex]
This simplifies to:
[tex]\[ 4y + 6 = 26 \][/tex]
2. Isolate the Variable Term:
Next, subtract 6 from both sides to isolate the term containing \( y \):
[tex]\[ 4y + 6 - 6 = 26 - 6 \][/tex]
This simplifies to:
[tex]\[ 4y = 20 \][/tex]
3. Solve for the Variable:
Finally, divide both sides by 4 to solve for \( y \):
[tex]\[ y = \frac{20}{4} \][/tex]
This simplifies to:
[tex]\[ y = 5 \][/tex]
Therefore, the solution to the equation \( y + 6 = -3y + 26 \) is \( y = 5 \).
Now, let's identify which choice matches this result:
Given choices:
1. \( y = -8 \)
2. \( y = -5 \)
3. \( y = 5 \)
4. \( y = 8 \)
The correct choice is [tex]\( y = 5 \)[/tex], which corresponds to the third choice.
1. Combine Like Terms:
[tex]\[ y + 6 = -3y + 26 \][/tex]
To isolate the variable \( y \) on one side, add \( 3y \) to both sides:
[tex]\[ y + 3y + 6 = 26 \][/tex]
This simplifies to:
[tex]\[ 4y + 6 = 26 \][/tex]
2. Isolate the Variable Term:
Next, subtract 6 from both sides to isolate the term containing \( y \):
[tex]\[ 4y + 6 - 6 = 26 - 6 \][/tex]
This simplifies to:
[tex]\[ 4y = 20 \][/tex]
3. Solve for the Variable:
Finally, divide both sides by 4 to solve for \( y \):
[tex]\[ y = \frac{20}{4} \][/tex]
This simplifies to:
[tex]\[ y = 5 \][/tex]
Therefore, the solution to the equation \( y + 6 = -3y + 26 \) is \( y = 5 \).
Now, let's identify which choice matches this result:
Given choices:
1. \( y = -8 \)
2. \( y = -5 \)
3. \( y = 5 \)
4. \( y = 8 \)
The correct choice is [tex]\( y = 5 \)[/tex], which corresponds to the third choice.
