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Select the correct answer.

A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?

[tex]$
\frac{9}{2} + 3(4-1) - 7 + 2^3
$[/tex]

Step 1: [tex]\( = \frac{9}{2} + 3(3) - 7 + 2^3 \)[/tex]

Step 2: [tex]\( = \frac{9}{2} + 3(3) - 7 + 8 \)[/tex]

Step 3: [tex]\( = \frac{15}{2} + 3(3) - 7 + 8 \)[/tex]

Step 4: [tex]\( = \frac{45}{2} - 7 + 8 \)[/tex]

Step 5: [tex]\( = \frac{31}{2} + 8 \)[/tex]

Step 6: [tex]\( = \frac{47}{2} \)[/tex]

A. Step 1
B. Step 4
C. Step 3
D. Step 5



Answer :

GinnyAnswer
Let's review each step in detail to locate the mistake.

Given expression:
[tex]\[ \frac{9}{2} + 3(4-1) - 7 + 2^3 \][/tex]

Step 1:
[tex]\[ \frac{9}{2} + 3(4-1) - 7 + 2^3 = \frac{9}{2} + 3(3) - 7 + 2^3 \][/tex]
This step looks correct, where [tex]\(4 - 1 = 3\)[/tex].

Step 2:
[tex]\[ \frac{9}{2} + 3(3) - 7 + 2^3 = \frac{9}{2} + 3(3) - 7 + 8 \][/tex]
This step is also correct because [tex]\(2^3 = 8\)[/tex].

Step 3:
[tex]\[ \frac{9}{2} + 3(3) - 7 + 8 = \frac{15}{2}(3) - 7 + 8 \][/tex]
This step is incorrect. The correct simplification of [tex]\(\frac{9}{2} + 3(3) - 7 + 8\)[/tex] should be:
[tex]\[ \frac{9}{2} + 9 - 7 + 8 \][/tex]

Clearly, a simplification error was introduced here. Let's verify this by double-checking the correct sequence of steps:

Correct intermediate step:
[tex]\[ \frac{9}{2} + 9 - 7 + 8 \][/tex]

So, the answer is:
The mistake occurs in Step 3.

Therefore, the correct answer is:
C. Step 3

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