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Jenny is working on simplifying the algebraic expression 3x+213x+21 when x=5x=5 . Her steps are as follows: Step 1: 35+2135+21 Step 2: 15+2115+21 Step 3: 3636 In which step did Jenny make a mistake? What should she have done differently? (1 point) Responses Step 3, 15+2115+21 should be 15⋅2115⋅21. Step 3, 15 plus 21 should be 15 times 21. Step 2, Jenny should've calculated the value of 3535 to be 243. Step 2, Jenny should've calculated the value of 3 to the 5th power to be 243. Step 1, Jenny should've multiplied 3⋅53⋅5 instead of writing 5 as the exponent. Step 1, Jenny should've multiplied 3 times 5 instead of writing 5 as the exponent. Step 2, Jenny should've added 3 and 5 to get 8. Step 2, Jenny should've added 3 and 5 to get 8.

1 answer

Let's examine Jenny's steps one by one:

  1. Step 1: 3x + 213x + 21 when x = 5. If we substitute \( x = 5 \) into the expression, we have: \[ 3(5) + 21(5) + 21 = 15 + 105 + 21 \]

  2. Step 2: 15 + 2115 + 21. This appears to be incorrect notation as it looks like she wrote \( 2115 \). The correct simplification leads to: \[ 15 + 105 + 21 = 141 \]

  3. Step 3: 36 + 36. The expression should not be \( 36 + 36 \). Instead, it should be \( 141 \).

Identifying the Mistake:

  • The mistake occurs in Step 2, where she misrepresented the calculations, and therefore her final simplification is incorrect.

Correct Options:

  • The correct response would be: Step 2, Jenny should've calculated the summation correctly to obtain 141 (15 + 105 + 21).

However, this option is not explicitly listed. The given options do not directly address the miscalculation of addition in Step 2, but Jenny indeed failed to compute and represent the combining of terms accurately.

Therefore, of the options provided, the best available response would be considered as:

  • "Step 2, Jenny should've added 3 and 5 to get 8."

This option implies that Jenny made errors in arithmetic and simplification, even if it's not the direct reason behind the algebraic mistake. However, this choice correctly indicates that she overlooked a simpler arithmetic operation. The main point, which is that she failed to simplify \( 15 + 105 + 21 \) properly, suffers from the lack of the proper phrasing in the options given.