Question

nathaniel writes the general form of the equation \\(gm = cm + rg\\) for when the equation is solved for \\(m\\). he uses the general form to solve the equation \\(-3m = 4m - 15\\) for \\(m\\). which expression shows what nathaniel will actually evaluate?

\\(4 + 15 - 3\\)
\\(4 - 15 + 3\\)
\\(\frac{-15}{-3 - 4}\\)
\\(-15 - \frac{-3}{4}\\)

Explanation:

Solve the general literal equation for m

Using the Literal Equations and Algebraic Rearrangement knowledge points

$$
LATEXBLOCK0
$$

Map the specific equation to the general form

Using the Literal Equations and Algebraic Rearrangement knowledge points

$$
LATEXBLOCK1
$$

Substitute the mapped values into the general solution

Using the Literal Equations and Algebraic Rearrangement knowledge points

$$
LATEXBLOCK2
$$

Analyze the incorrect options

Using the Literal Equations and Algebraic Rearrangement knowledge points

• Option A and B are simple arithmetic expressions that do not represent the division required by the solution.
• Option D represents a misinterpretation of the algebraic structure, isolating terms incorrectly.
• Option C correctly represents the substitution of the values into the solved general formula.

Answer:

• (A) \(4 + 15 - 3\)
• (B) \(4 - 15 + 3\)
• (C) \(\frac{-15}{-3-4}\) (Correct answer)
• (D) \(-15 - \frac{-3}{4}\)