What is the value of x that satisfies the inequality 4x + 12 < 16 + 8x?

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To solve the inequality 4x + 12 < 16 + 8x, we need to isolate x on one side. Here’s how we can do it step by step:

  1. Start with the original inequality:

    2. 4x + 12 < 16 + 8x

  2. To get all the x terms on one side and constant terms on the other side, subtract 4x from both sides:

    3. 12 < 16 + 8x – 4x

  3. This simplifies to:

    4. 12 < 16 + 4x

  4. Next, subtract 16 from both sides to isolate the term with x:

    5. 12 – 16 < 4x

  5. This further simplifies to:

    6. -4 < 4x

  6. To solve for x, divide both sides by 4:

    7. -1 < x

  7. This can be rewritten as:

    8. x > -1

Therefore, the solution set for the inequality is all values of x that are greater than -1.

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