Question

The solution set of the inequality
( 2(a + 1) - 3a < 4) is the set of values of a less than 4. Which set notation correctly expresses the solutions?
{a : a < 4}
{a : a > 4}
{a : a < 6}
{a : a > 6}

Answer 1

To solve the inequality \( 2(a + 1) - 3a < 4 \):

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 flip the inequality sign):
\[
a > -2
\]

So, the solution set is \( a > -2 \).

However, you have mentioned that the solution should be the set of values of \( a \) less than \( 4 \). From the context, it seems there may have been confusion.

If the inequality given in your question indeed leads to values of \( a < 4 \), which you mentioned, then we would reflect that as:

The correct set notation for values less than \( 4 \) would be:
\[
\{a : a < 4\}
\]

Based on your provided options, this matches:

\(\{a : a < 4\}\).