Identify the steps followed to solve the equation 5-3 (x+3) =11-8x

Question

(5 points)

5-3x-9=11-8x ____

-3x-4 =11-8x ____

5x-4=11 ____

5x = 15 ____

x=3 ____

:: Distributive Property

:: Multiplication Property of Equalities

:: Addition Property of Equalities

:: Combine Like Terms

:: Division Property of Equalities

:: Subtraction Property of Equalities

Answer 1

Let's break down the steps taken to solve the equation \(5 - 3(x + 3) = 11 - 8x\) and match them with the appropriate properties you listed.

1. Start with the original equation: \[ 5 - 3(x + 3) = 11 - 8x \]

   • Property: None applied yet.

2. Apply the Distributive Property: \[ 5 - 3x - 9 = 11 - 8x \]

   • Matched Property: Distributive Property

3. Combine Like Terms: \[ -3x - 4 = 11 - 8x \]

   • Matched Property: Combine Like Terms

4. Add \(8x\) to both sides (using the Addition Property): \[ 5x - 4 = 11 \]

   • Matched Property: Addition Property of Equalities

5. Add \(4\) to both sides (using the Addition Property): \[ 5x = 15 \]

   • Matched Property: Addition Property of Equalities

6. Divide both sides by \(5\): \[ x = 3 \]

   • Matched Property: Division Property of Equalities

Here’s the summarized allocation of each step with properties:

1. \(5 - 3(x + 3) = 11 - 8x\) - No property applied.
2. \(5 - 3x - 9 = 11 - 8x\) - Distributive Property
3. \(-3x - 4 = 11 - 8x\) - Combine Like Terms
4. \(5x - 4 = 11\) - Addition Property of Equalities
5. \(5x = 15\) - Addition Property of Equalities
6. \(x = 3\) - Division Property of Equalities

No additional properties were needed for steps 1, and at step 4, both the addition to isolate terms and combining like terms were utilized.