Hosni gave the following argument that 2(a 1 b) 5
2a 1 2b, for all integers a and b. If the argument is
correct, supply the missing reasons. If it is incorrect,
explain why not
To determine whether Hosni's argument is correct, we need to examine the steps he took and check if they are valid. Let's analyze each step of the argument:
Step 1: 2(a + b) = 5 (given)
Step 2: 2a + 2b (missing reason)
Conclusion: Therefore, 2a + 2b = 5 (assuming Hosni's argument is correct)
Now, let's evaluate whether each step of the argument is valid:
Step 1: The given equation is 2(a + b) = 5. This equation is not enough to establish a relationship between the terms 2a + 2b and 5. Therefore, the missing reason here is insufficient evidence.
Conclusion: Since the argument is based on an incorrect step, the conclusion is not valid. Therefore, Hosni's argument is incorrect.
In summary, the missing reason in Hosni's argument is that there is insufficient evidence to conclude that 2(a + b) equals 2a + 2b.