Solving an Inequality with Variables

Solve the inequality: -0.25 + 1.75x < -1.75 + 2.25x

Steps to Solve the Inequality:

To solve the given inequality, we need to isolate the variable x to determine its possible values. Follow these steps to find the solution:

  1. Subtract 1.75x from both sides of the inequality:

    2. -0.25 + 1.75x - 1.75x < -1.75 + 2.25x - 1.75x

    -0.25 < -1.75 + 0.5x

  2. Add 1.75 to both sides of the inequality:

    3. -0.25 + 1.75 < -1.75 + 0.5x + 1.75

    1.5 < -0.75 + 0.5x

  3. Add 0.75 to both sides of the inequality:

    4. 1.5 + 0.75 < -0.75 + 0.5x + 0.75

    2.25 < 0.5x

  4. Divide by 0.5 to both sides of the inequality:

    5. 2.25 / 0.5 < 0.5x / 0.5

    4.5 < x

  5. Therefore, the solution to the inequality is x is greater than 4.5, which can be written as x > 4.5.
Can you explain why the solution to the inequality is x > 4.5?

The solution x > 4.5 is derived from the steps taken to isolate the variable x in the original inequality. By following the rules of algebra to simplify the inequality, we reach the conclusion that x must be greater than 4.5 in order for the inequality to hold true. This means that any value of x larger than 4.5 will satisfy the original inequality, while any value less than or equal to 4.5 will not satisfy it.

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