Question

The solution to the inequality 3x - 2 is less than 7 as x is less than you set notation to express the value of x that makes sense the inequality 3x - 2 is less than seven true

Answer 1

To solve the inequality \(3x - 2 < 7\), we can follow these steps:

1. **Add 2 to both sides**:
\[
3x - 2 + 2 < 7 + 2
\]
This simplifies to:
\[
3x < 9
\]

2. **Divide both sides by 3**:
\[
\frac{3x}{3} < \frac{9}{3}
\]
This simplifies to:
\[
x < 3
\]

Now we want to express the solution in set notation. The set of all values of \(x\) that satisfy this inequality is:
\[
(-\infty, 3)
\]

This means that \(x\) can take any value less than 3. Therefore, the solution to the inequality \(3x - 2 < 7\) is:
\[
\{ x \in \mathbb{R} \mid x < 3 \} \text{ or simply } (-\infty, 3)
\]