Question

Steven was solving the equation
Below are the steps Steven used to solve the equation. Which statement/reason4 (x+6)=2x-8 would justify Steven's Step 1 to Step 2?

Steven justify steps

Question 10 options:

Distributive property of equality


Subtraction property of equality


Addition property of equality


Division property of equality

Answer 1

To determine which property justifies Steven's step from the equation \( 4(x + 6) = 2x - 8 \) to the next step, we need to analyze what type of operation is being performed.

Assuming that Step 1 is the original equation \( 4(x + 6) = 2x - 8 \), and Step 2 involves simplification or manipulation of both sides of the equation:

1. If Steven applies the **Distributive Property** to the left side, it will result in \( 4x + 24 = 2x - 8 \). Therefore, this justifies moving from Step 1 to Step 2.
2. If the operation involved was moving terms from one side of the equation to the other, it could involve the **Subtraction Property of Equality** or **Addition Property of Equality**.
3. The **Division Property of Equality** would apply if he divided by a common factor in both sides of the equation.

Based on the normal sequence for solving an equation like this, if Step 2 involved simplifying \( 4(x + 6) \) by distributing the 4, then the correct justification is:

**Distributive property of equality.**