Question

select the correct answer.
what is the justification for step 2 in the solution process?
\\(10x - 25 - 3x = 4x - 1\\)
step 1: \\(7x - 25 = 4x - 1\\)
step 2: \\(\\ \\ \\ \\ \\ \\ 7x = 4x + 24\\)
\\(\bigcirc\\) a. the division property of equality
\\(\bigcirc\\) b. the addition property of equality
\\(\bigcirc\\) c. the subtraction property of equality
\\(\bigcirc\\) d. the multiplication property of equality

Explanation:

To find the justification for Step 2, we analyze the transition from Step 1 (\(7x - 25 = 4x - 1\)) to Step 2 (\(7x = 4x + 24\)). In Step 2, we added 25 to both sides of the equation from Step 1. The addition property of equality states that if \(a = b\), then \(a + c = b + c\) for any real number \(c\). Here, \(c = 25\), so adding 25 to both sides (to isolate the term with \(x\) on the left) follows the addition property of equality.

Answer:

B. the addition property of equality