Question

Identify the properties used to solve the equation: 5 - 3 (x + 3) = 11 - 8x
5x = 15
5 - 3x - 9 = 11 - 8x
x = 3
5x - 4 = 11
-3x - 4 = 11 - 8x

Answer 1

To solve the equation \(5 - 3 (x + 3) = 11 - 8x\), we can identify the properties and steps used to arrive at the solution.

1. **Distributive Property**: This property is used to eliminate the parentheses by distributing the \(-3\) across \((x + 3)\).
\[
5 - 3x - 9 = 11 - 8x
\]

2. **Combining Like Terms**: After applying the distributive property, we combine like terms on the left side.
\[
5 - 9 - 3x = 11 - 8x \implies -4 - 3x = 11 - 8x
\]

3. **Adding/Subtracting Terms**: We can add \(8x\) and \(4\) to both sides to isolate \(x\).
\[
-3x + 8x = 11 + 4 \implies 5x = 15
\]

4. **Division Property of Equality**: Divide by \(5\) to solve for \(x\).
\[
x = 3
\]

So overall, the properties used include the **Distributive Property**, **Combining Like Terms**, and the **Addition/Subtraction Property of Equality** followed by the **Division Property of Equality**.

The related intermediate steps and results show the following equations:
- \(5 - 3(x + 3) = 11 - 8x\) ➔ **Original Equation**
- \(5 - 3x - 9 = 11 - 8x\) ➔ **Distributing and combining**
- \(-3x - 4 = 11 - 8x\) ➔ **Rearranging terms**
- \(5x - 4 = 11\) ➔ **Simplifying**
- \(5x = 15\) ➔ **Isolating variable**
- \(x = 3\) ➔ **Final solution**

These steps reflect the algebraic manipulations and properties used to solve the equation.