Question

2x - 5 = 8x + 7

Solving Step
Property used

Answer 1

To solve the equation \(2x - 5 = 8x + 7\), we can follow these steps:

### Step 1: Isolate the variable
We'll start by getting all the terms involving \(x\) on one side and the constant terms on the other.

**Property Used**: Addition Property of Equality

Add \(5\) to both sides:

\[
2x - 5 + 5 = 8x + 7 + 5
\]

This simplifies to:

\[
2x = 8x + 12
\]

### Step 2: Move the \(x\) terms
Next, we'll move \(8x\) to the left side by subtracting \(8x\) from both sides.

**Property Used**: Addition Property of Equality

Subtract \(8x\) from both sides:

\[
2x - 8x = 12
\]

This simplifies to:

\[
-6x = 12
\]

### Step 3: Solve for \(x\)
Now, divide both sides by \(-6\) to isolate \(x\).

**Property Used**: Division Property of Equality

\[
x = \frac{12}{-6}
\]

This simplifies to:

\[
x = -2
\]

### Summary of Steps and Properties Used:
1. **Step 1**: \(2x - 5 = 8x + 7\) → Add 5 to both sides.
- **Property Used**: Addition Property of Equality.

2. **Step 2**: \(2x = 8x + 12\) → Subtract \(8x\) from both sides.
- **Property Used**: Addition Property of Equality.

3. **Step 3**: \(-6x = 12\) → Divide by \(-6\).
- **Property Used**: Division Property of Equality.

Final solution: \(x = -2\).