Question

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solve the equation $3 = \dfrac{-7n + 5}{4}$ for $n$ by multiplying both sides of the equation by a value to rewrite the equation without the fraction, as in example 2.
multiply both sides of the equation by 4.
$\boxed{\quad} = -7n + 5$
isolate the variable term by subtracting a constant from both sides of the equation.
$\boxed{\quad} = -7n$
isolate the variable by dividing both sides by the same number.

Explanation:

Step1: Multiply both sides by 4

Given the equation \( 3 = \frac{-7n + 5}{4} \), we multiply both sides by 4 to eliminate the fraction.
\( 3\times4=\frac{-7n + 5}{4}\times4 \)
Simplifying, we get \( 12=-7n + 5 \).

Step2: Subtract 5 from both sides

To isolate the term with \( n \), we subtract 5 from both sides.
\( 12 - 5=-7n+5 - 5 \)
Simplifying, we get \( 7=-7n \).

Step3: Divide both sides by -7

To solve for \( n \), we divide both sides by -7.
\( \frac{7}{-7}=\frac{-7n}{-7} \)
Simplifying, we get \( n = - 1 \).

Answer:

\( n=-1 \)