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Henry used these steps to solve an equation:

Step 1: [tex]-3(x+2) = 5(x-7)[/tex]

Step 2: [tex]-3x - 6 = 5x - 35[/tex]

Step 3: [tex]-8x - 6 = -35[/tex]

Step 4: [tex]-8x = -29[/tex]

Step 5: [tex]x = \frac{29}{8}[/tex]

Between which two steps did Henry apply the distributive property?

A. steps 1 and 2

B. steps 2 and 3

C. steps 3 and 4

D. steps 4 and 5



Answer :

GinnyAnswer
To identify between which steps Henry applied the distributive property, let's carefully observe each step:

- Step 1: [tex]\(-3(x+2) = 5(x-7)\)[/tex]
- Step 2: [tex]\(-3x - 6 = 5x - 35\)[/tex]

Henry transformed the equation from Step 1 to Step 2 by distributing [tex]\(-3\)[/tex] over the terms inside the parentheses on the left and [tex]\(5\)[/tex] over the terms inside the parentheses on the right. This results in [tex]\(-3 \cdot x + (-3) \cdot 2 = 5 \cdot x + 5 \cdot (-7)\)[/tex], simplifying to:

[tex]\[ -3x - 6 = 5x - 35 \][/tex]

So, the distributive property was applied between steps 1 and 2. Thus, the correct answer is:

steps 1 and 2

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