How to Solve the Inequality 2x + 3 < 7 + 62x?

To solve the inequality 2x + 3 < 7 + 62x, we need to isolate the variable x. Let’s break this down step by step.

1. Start by simplifying both sides:
• On the left side, we have 2x + 3.
• On the right side, we have 7 + 62x.
2. Next, we will get all the x terms on one side and the constant terms on the other. To do this, we can subtract 2x from both sides:
• 2x + 3 – 2x < 7 + 62x - 2x
• This simplifies to 3 < 7 + 60x.
3. Now, subtract 7 from both sides:
• 3 – 7 < 60x
• This simplifies to -4 < 60x.
4. Next, divide both sides by 60. Since we are dividing by a positive number, the inequality direction remains the same:
• -4 / 60 < x
• This simplifies to -1/15 < x.
5. Finally, we can rewrite the solution:
• x > -1/15

In conclusion, the solution to the inequality 2x + 3 < 7 + 62x is x > -1/15.