How do I solve the inequality 3x < 2x + 1 and graph its solution on a number line?

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To solve the inequality 3x < 2x + 1, follow these steps:

  1. Start by isolating the variable on one side. Subtract 2x from both sides:
    • 3x – 2x < 1
    • This simplifies to:
    • x < 1
  2. The solution to the inequality is all values of x that are less than 1.

Now, let’s graph the solution on a number line:

-∞ +∞ 1

The open circle at x = 1 indicates that this value is not included in the solution. The shaded line to the left extends infinitely, representing all values less than 1.

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