Question

jalil and victoria are each asked to solve the equation \\(ax - c = bx + d\\) for \\(x\\). jalil says it is not possible to isolate \\(x\\) because each \\(x\\) has a different unknown coefficient. victoria believes there is a solution, and shows jalil her work:

1. \\(ax - c = bx + d\\)
2. \\(ax - bx = d + c\\)
3. \\(x(a - b) = d + c\\)
4. \\(x = \frac{d + c}{a - b}\\)

how can victoria justify step 3 of her work?

• rewrite the expression on the left using the distributive property.
• multiply both sides by \\(x\\).
• rewrite the expression on the left using subtraction.
• divide both sides by \\(x\\).

Explanation:

Analyze the transition from Step 2 to Step 3

Using the Literal Equations and Algebraic Rearrangement knowledge points

$$
LATEXBLOCK0
$$

Identify the algebraic property applied

Using the Algebraic Rearrangement knowledge point

$$ ax - bx = x(a - b) $$

Evaluate the given multiple-choice options

Using the Literal Equations knowledge point

• Option 1: Rewrite using distributive property.
• Option 2: Multiply both sides by \(x\).
• Option 3: Rewrite using subtraction.
• Option 4: Divide both sides by \(x\).

Answer:

• Rewrite the expression on the left using the distributive property. (Correct answer)
• Multiply both sides by \(x\).
• Rewrite the expression on the left using subtraction.
• Divide both sides by \(x\).