Answer :
Amir made an error in his calculations. Let's identify Amir's mistake and then solve the expression \(5x - (x + 3)^2\) correctly for \(x = 2\).
### Identify Amir's Mistake:
Amir's evaluation was:
[tex]\[ 5(2) - (2+3)^2 = 10 + (-5)^2 = 10 + 25 = 35 \][/tex]
- First, Amir correctly calculates the product \(5 \cdot 2\), which is \(10\).
- Next, he correctly computes \(2 + 3\), which gives \(5\).
- The mistake is in the part \((-5)^2\). Instead of correctly computing the square of \(5\), Amir mistakenly considers \( -5 \) and squares it, giving \( (-5)^2 = 25\). However, in the expression provided, there is no negative term.
### Correct Solution:
1. First term calculation:
[tex]\[ 5x \quad \text{for} \quad x = 2 \\ 5(2) = 10 \][/tex]
2. Second term calculation:
[tex]\[ (x + 3)^2 \quad \text{for} \quad x = 2 \\ (2 + 3)^2 = 5^2 = 25 \][/tex]
3. Combine the results:
[tex]\[ 5x - (x + 3)^2 = 10 - 25 \][/tex]
4. Final answer:
[tex]\[ 10 - 25 = -15 \][/tex]
The correct value of \(5x - (x + 3)^2\) for \(x = 2\) is \(-15\).
Hence, Amir's mistake was in the sign and calculation of the square term. The correct evaluation gives the result:
[tex]\[ 5(2) - (2 + 3)^2 = 10 - 25 = -15 \][/tex]
### Identify Amir's Mistake:
Amir's evaluation was:
[tex]\[ 5(2) - (2+3)^2 = 10 + (-5)^2 = 10 + 25 = 35 \][/tex]
- First, Amir correctly calculates the product \(5 \cdot 2\), which is \(10\).
- Next, he correctly computes \(2 + 3\), which gives \(5\).
- The mistake is in the part \((-5)^2\). Instead of correctly computing the square of \(5\), Amir mistakenly considers \( -5 \) and squares it, giving \( (-5)^2 = 25\). However, in the expression provided, there is no negative term.
### Correct Solution:
1. First term calculation:
[tex]\[ 5x \quad \text{for} \quad x = 2 \\ 5(2) = 10 \][/tex]
2. Second term calculation:
[tex]\[ (x + 3)^2 \quad \text{for} \quad x = 2 \\ (2 + 3)^2 = 5^2 = 25 \][/tex]
3. Combine the results:
[tex]\[ 5x - (x + 3)^2 = 10 - 25 \][/tex]
4. Final answer:
[tex]\[ 10 - 25 = -15 \][/tex]
The correct value of \(5x - (x + 3)^2\) for \(x = 2\) is \(-15\).
Hence, Amir's mistake was in the sign and calculation of the square term. The correct evaluation gives the result:
[tex]\[ 5(2) - (2 + 3)^2 = 10 - 25 = -15 \][/tex]
