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## Inequalities

### Mathematics, Grade 6

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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