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Chapter 4 Inequalities 4.1 Inequalities and Their Graphs An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: < A<B A is less than B. ≤ ≥ A>B A≤B A≥B A is greater than B. A is less than or equal to B. > A is greater than or equal to B. . Ex 1: Determine whether the given number is a solution of the inequality of x >4 a.) 4 4>4 False c.) -4 -4>4 False b.) 0 0>4 False d.) 6 6>4 True Graph the Inequality on the # line 1. Draw number line. Label zero and the number where your arrow starts 2. Put a circle on the number. Open Circle if < or >. Solid Circle if “or equal to” ≤or≥. 3. Draw your solution graph line in the same direction as the inequality IF the “x” is on left. Ex 2: Graph the solution of x > -2 -6 -4 -2 0 2 4 6 Ex 3: Graph the solution of x -2 If you have ≤ or ≥ you draw a closed circle -6 -4 -2 0 2 4 6 Hint: When graphing make sure your variable is on the left side 5<x To make sure the graph is correct switch the variable and number and flip the inequality. x>5 Now graph it -6 -4 -2 0 2 Ex 4: This is the graph of: -2 x > -2 x -2 x < -2 1) x 2) 3) 4) 4 6 -6 -4 -2 0 2 Ex 5: This is the graph of: 1 x > -1 x -1 x>1 1) x 2) 3) 4) 4 6 4.2 The Addition Property of Inequalities Addition Property of Inequalities If a < b, then a+c<b+c The same is true for >, , and Ex 6: Solve for “x”and graph: x-3>4 +3 +3 X>7 -8 -4 0 4 8 Ex 7: Solve for “x” and graph: 8z + 6 – 7z 16 Z + 6 16 -6 -6 z 10 -8 -4 0 4 8 1 1 Ex 8: Solve: x 3 4 4 3 x 12 12 3 4 x 12 12 7 x 12 Ex 9: 5(y-2)-4(y-1)<0 Assignment: Page 173 (4-18, 26-30) even Page 178 (8-36) even