Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)
4.5 - 7 = 2(y + 2.25) + 6.6
To solve this equation, we will follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
First, we will deal with the expressions inside the parentheses on the right side of the equation:
2(y + 2.25)
Using the distributive property, we can multiply 2 with y and 2.25:
2 * y + 2 * 2.25 = 2y + 4.5
Now we can rewrite the equation as:
4.5 - 7 = 2y + 4.5 + 6.6
Next, we can combine like terms on the right side:
4.5 - 7 = 2y + 11.1
Now, we need to simplify the left side by subtracting 7 from 4.5:
-2.5 = 2y + 11.1
To isolate the variable y, we need to get rid of the constant term 11.1. We can do this by subtracting 11.1 from both sides of the equation:
-2.5 - 11.1 = 2y + 11.1 - 11.1
-13.6 = 2y
Finally, to solve for y, we divide both sides of the equation by 2:
-13.6/2 = 2y/2
-6.8 = y
Therefore, the solution to the equation is y = -6.8.
We justified the solution using the properties of operations such as the distributive property and the simplification of expressions by combining like terms and reverse operations.