We need to solve the equation [tex]\(3x + 4 = 40\)[/tex] and determine who among Gembo and Pema will get the correct solution.
Let's analyze their steps one by one.
### Gembo's Method:
1. [tex]\(3x + 4 = 40\)[/tex]
2. [tex]\(x + 4 = \frac{40}{3}\)[/tex]
3. [tex]\(x = \frac{40}{3} - 4\)[/tex]
Gembo's first step is to subtract 4 from both sides, which should involve both terms on the left side. However, Gembo incorrectly divides the right-hand side by 3 only, leading to an incorrect simplification in step 2. This method is flawed because the division was applied incorrectly.
### Pema's Method:
1. [tex]\(3x + 4 = 40\)[/tex]
2. [tex]\(3x = 40 - 4\)[/tex]
3. [tex]\(x = \frac{40 - 4}{3}\)[/tex]
Pema correctly starts by subtracting 4 from both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ 3x = 40 - 4 \Rightarrow 3x = 36 \][/tex]
Then, Pema correctly divides both sides of the equation by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{36}{3} \Rightarrow x = 12 \][/tex]
### Conclusion:
Pema will get the correct solution. This conclusion is based on the correct application of algebraic steps. To verify, we substitute the solution back into the original equation:
[tex]\[ 3(12) + 4 = 36 + 4 = 40 \][/tex]
The left-hand side equals the right-hand side, confirming that [tex]\(x = 12\)[/tex] is indeed correct.
Therefore, Pema's approach is correct and yields the solution [tex]\(x = 12\)[/tex].
