To solve the inequality 3x < 2x + 1, we first aim to isolate x.
Step 1: Subtract 2x from both sides of the inequality:
3x – 2x < 2x + 1 – 2x
This simplifies to:
x < 1
Step 2: Now that we’ve solved for x, we need to represent this solution graphically on a number line.
To plot the solution x < 1, we place an open circle on the number 1. This indicates that 1 is not included in the solution. Then, we shade the line to the left of 1, showing all the values less than 1 are part of the solution.
Your number line should look like this:
——————–(1)——————->
In this number line representation, the open circle at 1 indicates that x = 1 is not a part of the solution set, whereas all the points to the left indicate valid solutions where x can be any value less than 1.