Solving linear inequalities in multi-step one variable is the same as solving multi-step linear equations begin by isolating the variable from the constants. If x > y and a > 0, then (x/a) > (y/a) and if x 0, then (x/a) y and a (y/a) Division Rule of Linear Inequalities:Īs per the division rule of linear inequalities, division of both sides of an inequality with a positive number produces an equivalent inequality, that is the inequality symbol does not change. If x > y, then x + a > y + a and if x y, then x − a > y − a and if x y and a > 0, then x × a > y × a and if x 0, then x × a y and a y × a. Addition Rule of Linear Inequalities:Īs per the addition rule of linear inequalities, adding the same number to each side of the inequality produces an equivalent inequality, that is the inequality symbol does not change. Before learning how to solve linear inequalities, let's look at some of the important rules of inequality for all these operations. All the rules mentioned below are also true for inequalities involving lesser than or equal to (≤), and greater than or equal to (≥). There are rules for both equality and inequality. Linear inequalities with the same solution are called equivalent inequality. The 4 types of operations that are done on linear inequalities are addition, subtraction, multiplication, and division. We can represent this inequality pictorially on a weighing scale as: We can see that the expression on the left-hand side, that is, 3x - 4 is in fact lesser than the number on the right-hand side, which is 20. Now, Let's say we have a linear inequality, 3x - 4 < 20. We need to note that if, p (greater than) and ≥ (greater than or equal to). The five symbols that are used to represent the linear inequalities are listed below: Symbol Name Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.
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