Survey

Survey

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4.1 Solving Linear Inequalities Objective: Solve and graph simple and compound inequalities in one variable. What are inequalities? Inequality Symbols • Greater than: > • Less than: < • Greater than or equal to: ≥ • Less than or equal to: ≤ Inequalities • Inequalities such as x ≤ 1 and p – 3 > 7 are linear inequalities in one variable. • A solution of an inequality in one variable is a value of the variable that makes the inequality true. • Example: -4, 0.7, and 1 are solutions of x ≤ 1 • Two inequalities are equivalent if they have the same solutions Properties of Inequalities • To write an equivalent inequality: • Add the same number to each side. • Subtract the same number from each side. • Multiply or divide each side by the same positive number. • Multiply or divide each side by the same negative number and reverse the inequality symbol. Solve the inequality. • x – 4 > -6 • -5y + 2 ≥ -13 Solve the inequality. • 7 – 4x < 1 – 2x • 2x – 3 > x Solve • -x + 3 ≤ -6 • x+3<8 • 3y – 5 < 10 • 2x – 3 > x Graphing Inequalities • The graph of an inequality in one variable consists of all points on a real number line that are solutions of the inequality. • To graph an inequality in one variable: • Use an open dot () for < or > • Use a solid dot () for ≤ or ≥ Graphing Inequalities • Graph x < 2 • Graph x ≥ 1 Solve the inequality and then graph your solution. • 4x + 3 ≤ 6x – 5 • -x + 2 < -3 Compound Inequalities A compound inequality is two simple inequalities joined by the word “and” or the word “or” AND All real numbers greater than or equal to -2 and less than 1 can be written as: OR All real numbers less than -1 or greater than or equal to 2 can be written as: -2 ≤ x < 1 Graph: x < -1 or x ≥ 2 Graph: Graph the Compound Inequality • x < -2 or x ≥ 3 • x ≤ -2 or x > 3 • -2 < x ≤ 3