Solving Algebraic Inequalities: Techniques And Graphical Representations

Algebraic inequality

It uses the inequality symbols instead of an equal; its algebraic because it has a variable 2y-5>14

An algebraic inequality is a statement that compares two algebraic expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). The inequality symbol indicates that one algebraic expression is lesser or greater than the other expression.

For example, consider the inequality x + 3 > 5. This inequality states that the sum of x and 3 is greater than 5. To solve this inequality, we need to isolate x on one side of the inequality symbol. We can do this by subtracting 3 from both sides, which gives us:

x > 2

This means that any value of x greater than 2 will satisfy the inequality. We can represent the solution set graphically on a number line by shading the region to the right of 2.

In general, to solve algebraic inequalities, we use the same rules and techniques as we would for solving algebraic equations, with the added step of identifying the direction of the inequality and representing the solution set graphically.

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