To solve the equation [tex]\(-11 - 12v = -6v + 19\)[/tex] step-by-step, let's analyze the properties we will use:
1. Addition Property of Equality: This property states that the same quantity can be added to both sides of an equation without changing the equality. We'll use this to isolate terms involving [tex]\(v\)[/tex] on one side of the equation.
2. Division Property of Equality: This property states that both sides of an equation can be divided by the same non-zero quantity without changing the equality. We'll use this to solve for [tex]\(v\)[/tex] once it's isolated.
3. Distributive Property: This property states that [tex]\(a(b + c) = ab + ac\)[/tex]. It allows us to distribute multiplication over addition or subtraction. Upon careful inspection of the given equation, the distributive property is irrelevant to solving this problem because there are no parentheses and no terms that require distribution.
Here's the step-by-step solution:
Step 1: Move all terms involving [tex]\(v\)[/tex] to one side by adding [tex]\(12v\)[/tex] to both sides and move the constant terms (numbers without [tex]\(v\)[/tex]) to the other side by adding 11 to both sides:
[tex]\[
-11 + 11 - 12v = -6v + 19 + 11
\][/tex]
Simplifies to:
[tex]\[
0 - 12v = -6v + 30
\][/tex]
or
[tex]\[
-12v = -6v + 30
\][/tex]
Step 2: Add [tex]\(6v\)[/tex] to both sides to combine like terms involving [tex]\(v\)[/tex]:
[tex]\[
-12v + 6v = -6v + 6v + 30
\][/tex]
Simplifies to:
[tex]\[
-6v = 30
\][/tex]
Step 3: Use the division property of equality to solve for [tex]\(v\)[/tex] by dividing both sides by [tex]\(-6\)[/tex]:
[tex]\[
v = \frac{30}{-6}
\][/tex]
Simplifies to:
[tex]\[
v = -5
\][/tex]
In this solution, we have used the Addition Property of Equality and the Division Property of Equality, but we did not use the Distributive Property.
Therefore, the property that will not be used in solving the equation [tex]\(-11 - 12v = -6v + 19\)[/tex] is the Distributive Property.
