Algebraic inequalities are mathematical statements that compare two quantities using inequality symbols such as <, >, ≤, or ≥.
To solve an algebraic inequality, you need to isolate the variable on one side of the inequality symbol and then perform the same operation on both sides of the inequality to maintain its balance. The solution is the set of values that satisfy the inequality.
The two main methods for solving algebraic inequalities are the graphical method and the algebraic method. In the graphical method, the solutions are represented on a number line. In the algebraic method, mathematical operations are used to isolate the variable and determine the solution.
Some common mistakes to avoid when solving algebraic inequalities include forgetting to flip the inequality symbol when multiplying or dividing both sides by a negative number, not distributing correctly when using the distributive property, and not properly simplifying the expressions on both sides of the inequality.
To check if the solution to an algebraic inequality is correct, you can substitute the solution back into the original inequality and see if it results in a true statement. You can also graph the solution on a number line and see if it satisfies the given inequality.
