Question

(2(a+1)-3a < 4) a is greater than four b it's less than four c it's greater than 6 or d it's less than 6

Answer 1

To solve the inequality \( 2(a + 1) - 3a < 4 \), let's simplify it step by step:

1. Distribute the \(2\):
\[
2a + 2 - 3a < 4
\]

2. Combine like terms:
\[
-a + 2 < 4
\]

3. Subtract \(2\) from both sides:
\[
-a < 2
\]

4. Multiply both sides by \(-1\) (remember to reverse the inequality):
\[
a > -2
\]

Now, let's analyze the options provided:
- (a) is greater than four
- (b) it's less than four
- (c) it's greater than 6
- (d) it's less than 6

Since the solution we found is \( a > -2 \), this means that \( a \) can be any value greater than \(-2\). This includes values less than 4 as well as values greater than 4. Thus, the correct conclusion is that:

- \( a < 4 \) (option (b)) is correct, but it doesn't encompass all possible solutions, only a part of it.

However, the only strict answer provided is that \(a\) can be greater than 4. Therefore, the conclusion is more general \( a > -2\), but from the options, only:
- (a) is a possible correct response based on the options provided, as \( a \) is indeed greater than 4.

So the best choice is:
**(a) it's greater than four.**