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Inequalities

Mathematics, Grade 9

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• An inequality is a mathematical sentence that does not have an exact solution. Instead, a range of solutions will satisfy the inequality. • All the solutions of an inequality with more than one solution are called the solution set. • Inequalities are used in many real–world situations. An example is a driving speed sign with a number which tells you that your speed must be 65mph. • Graph each inequality separately. • Combine both graphs. • Solve an addition or subtraction inequality the same way as you would solve an equation. • When you multiply or divide both sides of an inequality by a negative integer, reverse the direction of the inequality symbol. Graphing Simple Inequalities Graphing Compound Inequalities Solving Inequalities by Adding or Subtracting Solving Inequalities by Multiplying or Dividing 4 groups of -3 = -12 0 9 x x + 3 5 x + 3 5 x 2 – 3 – 3 Example Meaning Symbol • greater than • more than • above • less than • fewer than • below • greater than or equal to • no less than • at least • less than or equal to • no more than • at most room capacity age – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 1 3 2 1 0 – 4 – 3 – 2 – 1 0 > 50 > > – > – 14 3 5 6 4 > – > > > –> – An inequality uses one of the following symbols, instead of an equal sign: An open circle is used when the variable is or a number. > > A closed circle is used when the variable is or a number. > > – – > x – 4 x 1 or > x – 2 y 1 > – > – x 1 > – x – 2 > x 2 > – > – > – > – – 2x 6 – 2x 6 – 2x 6 – 2 – 2 x – 3 > > > > © Copyright NewPath Learning. All Rights Reserved. 93-4702 www.newpathlearning.com Inequalities

• An inequality is a mathematical sentence that does not have an exact solution. Instead, a range of solutions will satisfy the inequality. • All the solutions of an inequality with more than one solution are called the so . • Inequal ities are used in many real–world situations. An example is a driving speed sign with a number which tells you that your speed must be 65mph. • Graph each inequality separately. • Combine both graphs. • Solve an addition or subtraction inequality the same way as you would solve an equation. • When you multiply or divide both sides of an inequality by a negative integer, revers ethe direction of the inequality . Graphing Simple Inequalities Graphing Compound Inequalities Solving Inequalities by Adding or Subtracting Solving Inequalities by Multiplying or Dividing Example Meaning Symbol • greater than • more than • above • less than • fewer than • below • greater than or equal to • no less than • at least • less than or equal to • no more than • at most room capacity age – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 5 – 4 – 3 – 2 – 1 5 4 3 2 1 0 – 1 3 2 1 0 – 4 – 3 – 2 – 1 0 > – An inequality uses one of the following symbols, instead of an equal sign: An op en circle is used when the variable is or a number. > > A c losed circle is used when the variable is or a number. > > – – > x – 4 x 1 or > x – 2 y 1 > – > – x 1 > – x – 2 > x + 3 5 x + 3 5 x 2 – 3 – 3 x 2 > – > – > – > – – 2x 6 – 2x 6 – 2x 6 x > > > © Copyright NewPath Learning. All Rights Reserved. 93-4702 www.newpathlearning.com Key Vocabulary Terms • closed circle • compound inequality • greater than • greater than or equal to • inequality • less than • less than or equal to • negative integer • open circle • simple inequality • solution • solution set • variable Inequalities \|xiBAHBDy01669kzU

Inequalities

Mathematics, Grade 9

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