Which of the following steps indicates the addition property of equality while solving the equation $-1-6 x=x-15$?
A) $-1-6 x+15=x-15+15$
B) $23-6 x-24=x-15$
C) $x=14 / 2$
D) $-1-6 x=x-15$
Answer (1)
The addition property of equality states that adding the same value to both sides of an equation maintains the equality.
Option A, − 1 − 6 x + 15 = x − 15 + 15 , adds 15 to both sides of the original equation.
Options B, C, and D do not demonstrate the addition property of equality.
Therefore, the correct answer is A .
Explanation
Understanding the Problem The question asks us to identify the step that demonstrates the addition property of equality when solving the equation − 1 − 6 x = x − 15 . The addition property of equality states that if a = b , then a + c = b + c for any real number c . We need to examine the given options and see which one adds the same value to both sides of the original equation.
Analyzing the Options Let's examine each option to see if it follows the addition property of equality.
Option A: − 1 − 6 x + 15 = x − 15 + 15 . This adds 15 to both sides of the original equation, so it demonstrates the addition property of equality.
Option B: 23 − 6 x − 24 = x − 15 . This simplifies to − 1 − 6 x = x − 15 , which is the original equation. It does not demonstrate the addition property of equality.
Option C: x = 14/2 . This is a simplified form of the solution and does not demonstrate the addition property of equality.
Option D: − 1 − 6 x = x − 15 . This is the original equation and does not demonstrate the addition property of equality.
Conclusion Therefore, option A is the correct answer.
Examples
The addition property of equality is a fundamental concept in algebra and is used extensively in solving equations. For example, if you want to determine how much money you need to add to your savings account to reach a specific goal, you can use the addition property of equality to solve for the unknown amount. Suppose you have $100 in your account and want to reach $500. The equation would be 100 + x = 500 , where x is the amount you need to add. Using the addition property of equality, you subtract 100 from both sides to find x = 400 .
