Question

-6y + 8 = y +9 - 7y - 1

4 solving steps and 4 property used

Answer 1

Let's solve the equation \(-6y + 8 = y + 9 - 7y - 1\) step by step, while also identifying the properties used in each step.

### Step 1: Simplify the right side
Combine like terms on the right side of the equation.

\[
y + 9 - 7y - 1 = (1y - 7y) + (9 - 1) = -6y + 8
\]

So the equation simplifies to:

\[
-6y + 8 = -6y + 8
\]

**Property Used: Combining Like Terms**

### Step 2: Add \(6y\) to both sides
Add \(6y\) to both sides of the equation to eliminate \(-6y\) on both sides:

\[
-6y + 6y + 8 = -6y + 6y + 8
\]

This simplifies to:

\[
8 = 8
\]

**Property Used: Addition Property of Equality**

### Step 3: Recognize the statement
We have \(8 = 8\), which is a true statement.

**Property Used: Identity Property of Equality**

### Step 4: Conclude the solution
Since \(8 = 8\) is always true, the equation holds for all values of \(y\). Thus, the solution is:

\[
\text{All values of } y \text{ are solutions.}
\]

**Property Used: Identity Property of Equality (in the context of infinite solutions)**

Thus, we conclude that the original equation is an identity, meaning it is true for all values of \(y\).