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

Question

give me the 4 solving steps and 4 propertys used

Answer 1

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: $$y=-6.8$$