Question

Which property of equality justifies the step for solving the equation that is displayed?
A) 4k - 5 = 2k and 8j - 2 = 3j
B) 4 = k/2 + 5 and 4j - 14/3 + 5 = 3
C) 3(m + 1) = 10 and 6n + 3 = 6 - n
D) 2(3g + 5) - 2g = 2(4 - g) and -36h/6 = 2

Answer 1

To identify which property of equality justifies the step for solving the equations displayed in your choices, we need to analyze how these equations were manipulated.

Here’s a brief overview of each property of equality:

1. **Addition Property of Equality** - If \( a = b \), then \( a + c = b + c \).
2. **Subtraction Property of Equality** - If \( a = b \), then \( a - c = b - c \).
3. **Multiplication Property of Equality** - If \( a = b \), then \( ac = bc \).
4. **Division Property of Equality** - If \( a = b \) and \( c \neq 0 \), then \( \frac{a}{c} = \frac{b}{c} \).

Now let’s analyze each choice:

A) **4k - 5 = 2k and 8j - 2 = 3j**: This appears to use a combination of subtraction and simplification.

B) **4 = k/2 + 5 and 4j - 14/3 + 5 = 3**: This shows an equation set up for a solution, likely using the subtraction property here as well.

C) **3(m + 1) = 10 and 6n + 3 = 6 - n**: This involves distributing and possibly manipulating, but it doesn’t clearly favor one property over another without context.

D) **2(3g + 5) - 2g = 2(4 - g) and -36h/6 = 2**: Here, various numbers and variables are manipulated, including possibly the distributive property and division.

From this analysis, it is difficult to determine the exact step being justified without knowing the precise step being discussed. However, if you can provide the step or context, I’d be able to pinpoint which property of equality is being used.

If you're looking for a general justification, common manipulations like moving terms (addition/subtraction) or multiplying/dividing both sides will fall under their respective properties. Please clarify what specific step is being addressed!