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: \[ { x \in \mathbb{R} \mid x < 3 } \text{ or simply } (-\infty, 3) \]