Linear inequalities are mathematical expressions that compare two values using an inequality symbol like less than (<), less than or equal to (≤), greater than (>), or greater than or equal to (≥). Inequalities can be solved algebraically or graphically, and they have many real-life applications, including economics, engineering, and science.

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## Formula

To solve a linear inequality, you need to isolate the variable (usually represented by "x") on one side of the inequality sign and keep the inequality sign pointing in the correct direction.

For example, let's consider the following inequality:

3x + 5 > 11

To isolate x, we can start by subtracting 5 from both sides:

3x > 6

Then, we divide both sides by 3:

x > 2

Therefore, the solution to this inequality is:

x > 2

## Example

Suppose a company produces a product for $10 and sells it for $15. The company's total profit (P) can be represented by the following inequality:

P = 15x - 10x - 500 ≥ 0

Where x is the number of units produced. We can solve for x by isolating x on one side of the inequality:

5x - 500 ≥ 0

5x ≥ 500

x ≥ 100

This means that the company needs to produce at least 100 units to make a profit.

The calculator will show the solution to the inequality in the form of x < k or x > k, where k is a constant value.

## Conclusion

Linear inequalities are important mathematical expressions with many applications in real life. By following the steps outlined in this tutorial, you should now have a better understanding of how to solve linear inequalities algebraically. You can also use our Solve Linear Inequalities Calculator to quickly and easily solve linear inequalities.

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