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].
