Question

2x-5=8x+7
Property used

Answer 1

To solve the equation \(2x - 5 = 8x + 7\), we will use the properties of equality and the distributive property.

### Steps:

1. **Add \(5\) to both sides** to isolate terms involving \(x\) on one side:

\[
2x - 5 + 5 = 8x + 7 + 5
\]
\[
2x = 8x + 12
\]

**Property Used:** Addition Property of Equality

2. **Subtract \(8x\) from both sides** to get all \(x\) terms on one side:

\[
2x - 8x = 8x - 8x + 12
\]
\[
-6x = 12
\]

**Property Used:** Addition Property of Equality

3. **Divide both sides by \(-6\)** to solve for \(x\):

\[
x = \frac{12}{-6}
\]
\[
x = -2
\]

**Property Used:** Division Property of Equality

### Conclusion:
The solution to the equation \(2x - 5 = 8x + 7\) is \(x = -2\).

### Summary of Properties Used:
- Addition Property of Equality
- Division Property of Equality