Solve the inequality and show the graph of the solution on number line: 3x - 2 < 2x + 1.

Solution:

Given, the linear inequality is 3x - 2 < 2x + 1

We have to solve the inequality and show the graph of the solution on the number line.

By grouping,

3x - 2 - 2x < 1

3x - 2x < 1 + 2

x(3 - 2 ) < 3

x < 3

The solution is (-∞, 3).

The graphical representation is

The red line shows the required graph. Here, 3 is not included in the graph.

Therefore, the solution is (-∞, 3).

Solve the inequality and show the graph of the solution on number line: 3x - 2 < 2x + 1.

Summary:

On solving the linear inequality 3x - 2 < 2x + 1 the solution is (-∞, 3).