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

Question

A) Distributive Property
B) Combine Like Terms
C) Multiplication Property of Equalities
D) Division Property of Equalities
E) Addition Property of Equalities
F) Subtraction Property of Equalities

Answer 1

To solve the equation \(5 - 3 (x + 3) = 11 - 8x\), we can follow these steps in order:

1. Distributive Property (A): Apply the distributive property to the left side: \[ 5 - 3(x + 3) = 5 - 3x - 9 \] So the equation becomes: \[ -3x - 4 = 11 - 8x \]

2. Combine Like Terms (B): Bring all \(x\) terms on one side and constant terms on the other. First, add \(8x\) to both sides: \[ -3x + 8x - 4 = 11 \] This simplifies to: \[ 5x - 4 = 11 \]

3. Addition Property of Equalities (E): Add \(4\) to both sides to isolate the term with \(x\): \[ 5x = 15 \]

4. Division Property of Equalities (D): Finally, divide both sides by \(5\): \[ x = 3 \]

The correct steps followed to solve the equation are:

1. Distributive Property (A)
2. Combine Like Terms (B)
3. Addition Property of Equalities (E)
4. Division Property of Equalities (D)

So the answer is:

• A, B, E, D.