![]() The polynomial inequalities are inequalities that can be expressed as a polynomial on one side and 0 on the other side of the inequality. Let us now see how to solve different types of inequalities and how to graph the solution in each case. ![]() You can see, y = x + 4 line and the shaded area (in yellow) is where y is less than or equal to x + 4. Let us try some example: This is a graph of a linear inequality: y ≤ x + 4 Shade the region above the line for a "greater than" (y> or y≥) or below the line for a "less than" (yHere are some examples to understand the same: Inequality Use always open bracket at either ∞ or -∞.If the endpoint is not included (i.e., in case of ), use the open brackets '(' or ')'.If the endpoint is included (i.e., in case of ≤ or ≥) use the closed brackets ''.While writing the solution of an inequality in the interval notation, we have to keep the following things in mind. Writing Inequalities in Interval Notation Draw a line from the endpoint that extends to the left side if the variable is lesser than the number.Draw a line from the endpoint that extends to the right side if the variable is greater than the number.If the endpoint is NOT included (i.e., in case of ), use an open circle.If the endpoint is included (i.e., in case of ≤ or ≥) use a closed circle.While graphing inequalities, we have to keep the following things in mind. Let us use this procedure to solve inequalities of different types. But to solve any other complex inequality, we have to use the following process. The process of solving inequalities mentioned above works for a simple linear inequality. Why? This is because we have multiplied both sides of the inequality by a negative number. Step - 7: Intervals that are satisfied are the solutions.īut for solving simple inequalities (linear), we usually apply algebraic operations like addition, subtraction, multiplication, and division.Step - 6: Take a random number from each interval, substitute it in the inequality and check whether the inequality is satisfied.Step - 4: Also, represent all excluded values on the number line using open circles.Step - 3: Represent all the values on the number line.Step - 2: Solve the equation for one or more values.Step - 1: Write the inequality as an equation. ![]() Here are the steps for solving inequalities: Multiplication or dividing both sides by a negative number Multiplying or dividing both sides by a positive number Operation Applied While Solving Inequalities The rules of inequalities are summarized in the following table. Taking a square root will not change the inequality. Putting minuses in front of p and q changes the direction of the inequality.Ī square of a number is always greater than or equal to zero p 2 ≥ 0.Įxample: (4) 2= 16, (−4) 2 = 16, (0) 2 = 0 Inequalities Rule 8 Positive case example: Oggy's score of 5 is lower than Mia's score of 9 (p −q. If you multiply both p and q by a negative number, the inequality swaps: p qd (inequality swaps) If you multiply numbers p and q by a positive number, there is no change in inequality. So, the addition and subtraction of the same value to both p and q will not change the inequality. Inequalities Rule 3Īdding the number d to both sides of inequality: If p q, then p + d > q + d, and Inequalities Rule 2Įxample: Oggy is older than Mia, so Mia is younger than Oggy. When inequalities are linked up you can jump over the middle inequality.Įxample: If Oggy is older than Mia and Mia is older than Cherry, then Oggy must be older than Cherry. Here are some listed with inequalities examples. There are different types of inequalities.
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