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Section 1.7 class notes_0

# Section 1.7 class notes_0 - number 1.7.3 Solve the linear...

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Section 1.7 Linear Inequalities Unlike equations which usually have a finite number of solutions (or no solution at all), inequalities often have infinitely many solutions. We typically describe the solutions to an inequality in one of three ways: 1) Graph the solution on a number line 2) Write the solution in set builder notation 3) Write the solution in interval notation Objective 1 : Solving Linear Inequalities Definition A linear inequality is an inequality that can be written in the form ax b c + < where a, b and c are real numbers and 0 a . Note: The inequality symbol “<” in the definition above and the properties below can be replaced with either >, , or . The technique to use when solving linear inequalities is to isolate the variable on one side. Remember to reverse the direction of the inequality when multiplying or dividing a linear inequality by a negative
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Unformatted text preview: number. 1.7.3 Solve the linear inequality and express the solution in set-builder notation. Simplify your answer. Use integers or fractions for any numbers in the expression. 1.7.6 Solve the linear inequality. Graph the solution set on a number line and express each solution using interval notation. Objective 2 : Solving Three-Part Inequalities The technique to use when solving three-part inequalities is to simplify until the variable is “sandwiched” in the middle. It is good practice to rewrite the inequality so that the smaller of the two outside numbers is on the left. A number is a solution to a three-part inequality if it is a solution to both inequalities. 1.7.12 Solve the three-part inequality. Graph the solution set on a number line and express each solution using interval notation....
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