Question

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Part 1
Solve the equation. Check your solution.
negative 4 left parenthesis 4 n minus 3 right parenthesis equals 32−4(4n−3)=32

Answer 1

Let's solve the equation step by step. The equation given is:

\[
-4(4n - 3) = 32
\]

First, distribute the negative 4 on the left side:

\[
-4 \cdot 4n + 4 \cdot 3 = 32
\]
\[
-16n + 12 = 32
\]

Next, we will isolate the term with \( n \) by subtracting 12 from both sides:

\[
-16n + 12 - 12 = 32 - 12
\]
\[
-16n = 20
\]

Now, we divide both sides by -16 to solve for \( n \):

\[
n = \frac{20}{-16}
\]
\[
n = -\frac{5}{4}
\]

Now, we will check our solution by substituting \( n = -\frac{5}{4} \) back into the original equation.

Substituting \( n \):

\[
-4(4(-\frac{5}{4}) - 3) = 32
\]

Calculating the expression inside the parentheses:

\[
4(-\frac{5}{4}) = -5
\]
\[
-5 - 3 = -8
\]

Now substituting back into the equation:

\[
-4(-8) = 32
\]
\[
32 = 32
\]

Since both sides of the equation are equal, our solution is verified.

Thus, the solution is:

\[
n = -\frac{5}{4}
\]