Question

property used in 2x-5=8x+7

Answer 1

To solve the equation \( 2x - 5 = 8x + 7 \), we can use several algebraic properties. Here's a step-by-step breakdown highlighting the properties used:

1. **Transposition (or Addition Property of Equality)**:
We can move terms from one side of the equation to the other by adding or subtracting. In this case, we will subtract \( 2x \) from both sides to start solving for \( x \):
\[
2x - 5 - 2x = 8x + 7 - 2x
\]
This simplifies to:
\[
-5 = 6x + 7
\]

2. **Transposition Again**:
Now we need to isolate \( 6x \) by subtracting \( 7 \) from both sides:
\[
-5 - 7 = 6x + 7 - 7
\]
This simplifies to:
\[
-12 = 6x
\]

3. **Division Property of Equality**:
To solve for \( x \), divide both sides by \( 6 \):
\[
\frac{-12}{6} = \frac{6x}{6}
\]
This yields:
\[
x = -2
\]

So the final solution is \( x = -2 \). Throughout this process, we utilized properties such as the addition property of equality and the division property of equality to isolate \( x \).