To solve the equation step by step, let's identify the operations involved in each transformation:
-
Original Equation: \( 5 - 3(x + 3) = 11 - 8x \)
- This is where we start.
-
Step 1: \( 5 - 3(x + 3) = 11 - 8x \)
- We apply the Distributive Property (A) to expand the left side:
- \( 5 - 3x - 9 = 11 - 8x \)
-
Step 2: \( 5 - 3x - 9 = 11 - 8x \)
- Now, combine like terms on the left side:
- Combine Like Terms (B) results in:
- \( -3x - 4 = 11 - 8x \)
-
Step 3: \( -3x - 4 = 11 - 8x \)
- We can add \( 8x \) to both sides to isolate \( x \). This applies the Addition Property of Equalities (E):
- \( -3x + 8x - 4 = 11 \) which simplifies to:
- \( 5x - 4 = 11 \)
-
Step 4: \( 5x - 4 = 11 \)
- Next, add \( 4 \) to both sides. This again uses the Addition Property of Equalities (E):
- \( 5x - 4 + 4 = 11 + 4 \) simplifies to:
- \( 5x = 15 \)
-
Step 5: \( 5x = 15 \)
- Now, divide by \( 5 \) to solve for \( x \). This applies the Division Property of Equalities (D):
- \( x = 3 \)
So, summarizing the steps:
- Step 1: A (Distributive Property)
- Step 2: B (Combine Like Terms)
- Step 3: E (Addition Property of Equalities twice: first to isolate \( x \), then to cancel \( -4 \))
- Step 4: D (Division Property of Equalities)
Thus, the correct operations used in each step in solving the equation are:
- A) Distributive Property
- B) Combine Like Terms
- E) Addition Property of Equalities
- D) Division Property of Equalities