Answer :
To solve the equation [tex]\(-12x = 48\)[/tex] using the division property of equality, follow these steps:
1. Understand the Division Property of Equality: This property states that you can divide both sides of an equation by the same nonzero number, and the equality will still hold true.
2. Apply the Division Property: To isolate the variable [tex]\(x\)[/tex], you need to divide both sides of the equation by [tex]\(-12\)[/tex] because [tex]\(-12\)[/tex] is the coefficient of [tex]\(x\)[/tex].
[tex]\[
\frac{-12x}{-12} = \frac{48}{-12}
\][/tex]
3. Simplify Both Sides:
- On the left side, [tex]\(\frac{-12x}{-12}\)[/tex] simplifies to [tex]\(x\)[/tex].
- On the right side, [tex]\(\frac{48}{-12}\)[/tex] simplifies to [tex]\(-4\)[/tex].
So, you get:
[tex]\[
x = -4
\][/tex]
4. Identify the Correct Choice: Among the given options, the expression [tex]\(\frac{-12x}{-12} = \frac{48}{-12}\)[/tex] represents the correct use of the division property of equality. Hence, the correct answer is option B.
Therefore, the solution indicates that option B) [tex]\(\frac{-12x}{-12} = \frac{48}{-12}\)[/tex] is the choice that applies the division property of equality correctly.
1. Understand the Division Property of Equality: This property states that you can divide both sides of an equation by the same nonzero number, and the equality will still hold true.
2. Apply the Division Property: To isolate the variable [tex]\(x\)[/tex], you need to divide both sides of the equation by [tex]\(-12\)[/tex] because [tex]\(-12\)[/tex] is the coefficient of [tex]\(x\)[/tex].
[tex]\[
\frac{-12x}{-12} = \frac{48}{-12}
\][/tex]
3. Simplify Both Sides:
- On the left side, [tex]\(\frac{-12x}{-12}\)[/tex] simplifies to [tex]\(x\)[/tex].
- On the right side, [tex]\(\frac{48}{-12}\)[/tex] simplifies to [tex]\(-4\)[/tex].
So, you get:
[tex]\[
x = -4
\][/tex]
4. Identify the Correct Choice: Among the given options, the expression [tex]\(\frac{-12x}{-12} = \frac{48}{-12}\)[/tex] represents the correct use of the division property of equality. Hence, the correct answer is option B.
Therefore, the solution indicates that option B) [tex]\(\frac{-12x}{-12} = \frac{48}{-12}\)[/tex] is the choice that applies the division property of equality correctly.
