Question

Trinity solved the equation 2(x - 3) + 7 - 3x - 11. Match the steps (1-5) and the correct justification below.

Given
2(x - 3) + 7 - 3x - 11
Step 1:
2x - 6 + 7 - 3x - 11
Step 2:
2x - 3x - 6 + 7 = 11
Step 3:
-x + 1 - 11
Step 4:
-x - 10
Step 5:
x = -10

A. Addition Property of Equality
B. Multiplication Property of Equality
C. Wrote equivalent expression
D. Distributive Property
E. Commutative Property of Addition

Answer 1

To solve the equation 2(x - 3) + 7 - 3x - 11, you need to simplify the expression step by step using properties of equality. The final solution is x = -10.

Step-by-step explanation:

1. Given equation: 2(x - 3) + 7 - 3x - 11
2. Apply the Distributive Property: 2x - 6 + 7 - 3x - 11
3. Combine like terms: 2x - 3x - 6 + 7 = 11
4. Simplify further: -x + 1 - 11
5. Combine like terms: -x - 10
6. Apply the Addition Property of Equality: x = -10