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?

$\boldsymbol{-15 - \frac{-3}{4}}$ $\boldsymbol{\frac{-15}{-3 - 4}}$ $\boldsymbol{4 + 15 - 3}$

$\boldsymbol{4 - 15 + 3}$

Explanation:

Step1: Solve \( gm = cm + rg \) for \( m \)

Subtract \( cm \) from both sides: \( gm - cm = rg \)
Factor out \( m \): \( m(g - c) = rg \)
Divide both sides by \( g - c \): \( m = \frac{rg}{g - c} \)

Step2: Apply to \( -3m = 4m - 15 \)

Rewrite the equation: \( -3m - 4m = -15 \) (subtract \( 4m \) from both sides)
Simplify left side: \( -7m = -15 \), or compare to \( gm = cm + rg \):
Here, \( g = -3 \), \( c = 4 \), \( rg = -15 \).
Substitute into \( m = \frac{rg}{g - c} \): \( m = \frac{-15}{-3 - 4} \)

Answer:

\(\frac{-15}{-3 - 4}\) (matches the second option)