Sure, let's solve the equation \(2y = 12 - 5x\) for \(y\) when \(x = -2\).
1. Substitute \(x = -2\) into the equation:
[tex]\[
2y = 12 - 5(-2)
\][/tex]
2. Calculate \(5(-2)\):
[tex]\[
5 \times -2 = -10
\][/tex]
Since \( 5 \times -2 \) equals \(-10\),
3. Substitute the result of \(5(-2)\) back into the equation:
[tex]\[
2y = 12 - (-10)
\][/tex]
4. Simplify the right-hand side of the equation:
[tex]\[
12 - (-10) = 12 + 10 = 22
\][/tex]
So now the equation is:
[tex]\[
2y = 22
\][/tex]
5. Solve for \(y\) by dividing both sides of the equation by 2:
[tex]\[
y = \frac{22}{2}
\][/tex]
6. Calculate the division:
[tex]\[
y = 11
\][/tex]
Therefore, the value of \(y\) that satisfies the equation \(2 y = 12 - 5 x\) when \(x = -2\) is \( y = 11\).
The correct answer is:
C) 11
