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:

-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:

-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:

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:

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.

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.