To solve the equation \( 5 - 3(x + 3) = 11 - 8x \) and follow the steps you provided, we can break down the process while noting the properties used.
Step-by-Step Breakdown
Step 1: Apply the Distributive Property
- Start with the original equation: \[ 5 - 3(x + 3) = 11 - 8x \]
- Distributing \( -3 \) across \( (x + 3) \): \[ 5 - 3x - 9 = 11 - 8x \]
Property Used: Distributive Property
Step 2: Combine Like Terms
- Now simplify the left side: \[ (5 - 9) - 3x = 11 - 8x \]
- This simplifies to: \[ -4 - 3x = 11 - 8x \]
Property Used: Combine Like Terms
Step 3: Isolate Terms with x
- Add \( 3x \) to both sides to get all x-terms on one side: \[ -4 = 11 - 8x + 3x \]
- This results in: \[ -4 = 11 - 5x \]
Property Used: Addition Property of Equality
Step 4: Isolate the Constant
- Now, subtract \( 11 \) from both sides: \[ -4 - 11 = -5x \]
- This gives: \[ -15 = -5x \]
Property Used: Subtraction Property of Equality
Step 5: Solve for x
- Now, divide both sides by \( -5 \): \[ x = \frac{-15}{-5} = 3 \]
Property Used: Division Property of Equality
Final Solution
The solution to the equation \( 5 - 3(x + 3) = 11 - 8x \) is: \[ x = 3 \]
Summary of Properties Used
- Distributive Property (Step 1)
- Combine Like Terms (Step 2)
- Addition Property of Equality (Step 3)
- Subtraction Property of Equality (Step 4)
- Division Property of Equality (Step 5)
37 answers