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Instructions: Solve for [tex]\( n \)[/tex], given the equation [tex]\(-3(2n - 3) = 25 - 8n\)[/tex].

\begin{tabular}{|l|l|l|}
\hline
\multicolumn{1}{|c|}{Step} & \multicolumn{1}{c|}{Explanation} & \multicolumn{1}{c|}{Property} \\
\hline
[tex]\(-3(2n - 3) = 25 - 8n\)[/tex] & Given equation & \\
\hline
[tex]\(-6n + 9 = 25 - 8n\)[/tex] & Distribute [tex]\(-3\)[/tex] into [tex]\((2n - 3)\)[/tex] & \\
\hline
[tex]\(-6n + 9 - 9 = 25 - 8n - 9\)[/tex] & Subtract 9 from both sides & \\
\hline
[tex]\(-6n = -8n + 16\)[/tex] & Combine like terms & Simplify \\
\hline
[tex]\(-6n + 8n = -8n + 16 + 8n\)[/tex] & Add [tex]\(8n\)[/tex] to both sides & \\
\hline
[tex]\(2n = 16\)[/tex] & Combine like terms & Simplify \\
\hline
[tex]\(\frac{2n}{2} = \frac{16}{2}\)[/tex] & Divide by 2 on both sides & \\
\hline
[tex]\(n = 8\)[/tex] & Final solution & \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
Let's solve the equation step-by-step to find the value of [tex]\( n \)[/tex]. Each step will include the necessary explanations and corresponding properties.

### Step 1: Given Equation
[tex]\[ -3(2n - 3) = 25 - 8n \][/tex]
Explanation: This is the equation provided in the question.
Property: Given.

### Step 2: Distribute
[tex]\[ -6n + 9 = 25 - 8n \][/tex]
Explanation: Distribute the [tex]\(-3\)[/tex] into the terms inside the parentheses.
Property: Distributive Property.

### Step 3: Subtract 9 from Both Sides
[tex]\[ -6n + 9 - 9 = 25 - 8n - 9 \][/tex]
Explanation: Subtract 9 from both sides to simplify the equation.
Property: Subtraction Property of Equality.

### Step 4: Simplify
[tex]\[ -6n = 25 - 8n + 16 \][/tex]
Explanation: Combine like terms on both sides of the equation.
Property: Combine like terms.

### Step 5: Add [tex]\(8n\)[/tex] to Both Sides
[tex]\[ -6n + 8n = 16 - 8n + 8n \][/tex]
Explanation: Add [tex]\( 8n \)[/tex] to both sides to start isolating [tex]\( n \)[/tex].
Property: Addition Property of Equality.

### Step 6: Simplify
[tex]\[ 2n = 16 \][/tex]
Explanation: Combine like terms on both sides.
Property: Combine like terms.

### Step 7: Divide by 2 on Both Sides
[tex]\[ \frac{2n}{2} = \frac{16}{2} \][/tex]
Explanation: Divide both sides by 2 to solve for [tex]\( n \)[/tex].
Property: Division Property of Equality.

### Final Solution
[tex]\[ n = \frac{16}{2} \][/tex]
[tex]\[ n = 8 \][/tex]

So, the value of [tex]\( n \)[/tex] that satisfies the equation [tex]\( -3(2n-3)=25-8n \)[/tex] is [tex]\( n = 8 \)[/tex].
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