Linear Inequality Solver
Solve linear inequalities and visualize the solution on a number line.
Use this Inequality Solver, Linear Inequality Solver, Inequality Calculator, Solve Inequalities, Inequality Solution calculator for quick, clear estimates. Try a tiny example to see the impact of each input.
Q: What is an inequality in math?
In mathematics, an inequality is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠(not equal to). Unlike equations, which show equality, inequalities show that one expression is not equal to another.
How do you solve a linear inequality?
Solving a linear inequality is similar to solving a linear equation, with one crucial difference: if you multiply or divide both sides of the inequality by a negative number, you must reverse the direction of the inequality sign. Otherwise, you use inverse operations to isolate the variable, just as you would with an equation.
What are the rules for inequalities?
The main rules for inequalities are:
1. You can add or subtract the same number from both sides without changing the inequality direction.
2. You can multiply or divide both sides by a positive number without changing the inequality direction.
3. If you multiply or divide both sides by a negative number, you must reverse the direction of the inequality sign.
4. The transitive property also applies: if a < b and b < c, then a < c.
What is the solution set for an inequality?
The solution set for an inequality is the range of all real numbers that, when substituted for the variable, make the inequality a true statement. Unlike equations which often have a single solution, inequalities typically have an infinite number of solutions, which are often expressed using interval notation or by graphing the solution on a number line.