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4.5 - 7 = 2(y + 2.25) + 6.6

give me the 4 solving steps and 4 propertys used

1 answer

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:

  1. Subtraction of real numbers: To simplify \(4.5 - 7\).
  2. Distributive property: To distribute \(2\) across \(y + 2.25\).
  3. Addition of real numbers: To combine \(4.5\) and \(6.6\).
  4. Division of real numbers: To solve for \(y\) after isolating it.

The final solution is: \[ y = -6.8 \]