How do I solve the inequality 2x + 20 < 37 + 62x?

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To solve the inequality 2x + 20 < 37 + 62x, we’ll need to follow a series of steps to isolate x:

  1. Reorganize the inequality: Start by getting all the terms involving x on one side and the constants on the other. We can subtract 2x from both sides:
  2. Subtract 2x from both sides: This yields:

    3. 20 < 37 + 60x

  3. Next, isolate the 60x: Now we will subtract 37 from both sides:

    4. 20 – 37 < 60x

  4. Simplify the left side: Calculate 20 – 37:

    5. -17 < 60x

  5. Divide by 60: To find x, divide both sides by 60, keeping in mind that dividing by a positive number does not change the direction of the inequality:

    6. -17/60 < x

  6. Final Result: The solution can be expressed as:

    7. x > -17/60

Conclusion: The inequality tells us that x must be greater than -17/60 for the original inequality to hold true.

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