Question

2x - 5 = 8x + 7

give me the 4 solving steps and 4 property used

Answer 1

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

### Steps to Solve:

1. **Isolate the variable on one side**:
\[
2x - 5 = 8x + 7
\]
Add \( -8x \) and \( 5 \) to both sides:
\[
2x - 8x - 5 + 5 = 7 + 5
\]
This simplifies to:
\[
-6x = 12
\]

2. **Multiply or divide to solve for the variable**:
\[
-6x = 12
\]
Divide both sides by \(-6\):
\[
x = \frac{12}{-6}
\]
This simplifies to:
\[
x = -2
\]

3. **Check the solution**:
Substitute \( x = -2 \) back into the original equation:
\[
2(-2) - 5 = 8(-2) + 7
\]
This gives:
\[
-4 - 5 = -16 + 7
\]
Simplifying both sides:
\[
-9 = -9
\]
This confirms that our solution is correct.

4. **State the final answer**:
Thus, the solution to the equation is:
\[
x = -2
\]

### Properties Used:

1. **Addition Property of Equality**: If you add (or subtract) the same number to both sides of an equation, the two sides remain equal.

2. **Multiplication Property of Equality**: If you multiply (or divide) both sides of an equation by the same non-zero number, the two sides remain equal.

3. **Substitution Property**: If two values are equal, one can be substituted for the other in any expression or equation.

4. **Distributive Property** (implicitly used when combining like terms): This states that \( a(b + c) = ab + ac \) and helps in combining and simplifying terms in the equation.

These steps and properties lead us to the solution of the equation.