To solve the equation \(4.5 - 7 = 2(y + 2.25) + 6.6\), we can follow these steps:
Step 1: Simplify the left-hand side
Calculate \(4.5 - 7\).
\[ 4.5 - 7 = -2.5 \]
Now, the equation is:
\[ -2.5 = 2(y + 2.25) + 6.6 \]
Property Used: Subtraction of real numbers.
Step 2: Simplify the right-hand side
Distribute \(2\) into \(y + 2.25\).
\[ 2(y + 2.25) = 2y + 4.5 \]
Now, the equation will look like:
\[ -2.5 = 2y + 4.5 + 6.6 \]
Property Used: Distributive property.
Step 3: Combine like terms on the right-hand side
Add \(4.5\) and \(6.6\).
\[ 4.5 + 6.6 = 11.1 \]
Thus, we have:
\[ -2.5 = 2y + 11.1 \]
Property Used: Addition of real numbers.
Step 4: Isolate \(y\)
Subtract \(11.1\) from both sides:
\[ -2.5 - 11.1 = 2y \]
\[ -13.6 = 2y \]
Now, divide both sides by \(2\):
\[ y = -\frac{13.6}{2} = -6.8 \]
Property Used: Addition and division of real numbers.
Summary of Properties Used:
- Subtraction of real numbers: To simplify \(4.5 - 7\).
- Distributive property: To distribute \(2\) across \(y + 2.25\).
- Addition of real numbers: To combine \(4.5\) and \(6.6\).
- Division of real numbers: To solve for \(y\) after isolating it.
The final solution is: \[ y = -6.8 \]