Solving Linear & Graphing Inequalities Sep 7 11:06 PM 1
Open circle on the graph means that the inequality will be greater than or less than. > or < Closed circle on the graph means that the inequality will be greater than or equal to OR less equal than or equal. Sep 13 1:02 PM 2
If the direction of the GRAPH is pointed to the LEFT, then inequality is "less than" or "less than or equal to". 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 If the direction of the GRAPH is pointed to the RIGHT, then inequality is "greater than" or "greater than or equal to". 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Sep 13 1:08 PM 3
greater than side of any inequality > OR less than side of any inequality less than side of any inequality > greater than side of any inequality Oct 21 11:03 AM 4
EXAMPLE 1 Given the graph, below : a) Write a statement in words to express the graph on the number. b) Write an inequality to express the graph on the number line, use x as your variable. 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 SOLUTION a) All numbers less than 2. b) or Sep 13 12:58 PM 5
EXAMPLE 2 Given the graph, below : a) Write a statement in words to express the graph on the number. b) Write an inequality to express the graph on the number line, use x as your variable. 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 SOLUTION a) All numbers greater than or equal to 5. b) or Sep 13 1:23 PM 6
EXAMPLE 3 Solve the inequality, then graph the solution set on a number line. SOLUTION Oct 21 11:13 AM 7
+ 7 + 7 6 6 x 3 x is greater than or equal to 3 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Oct 21 11:20 AM 8
EXAMPLE 4 Solve the inequality, then graph the solution set on a number line. SOLUTION 23 < 7 5x Oct 21 11:25 AM 9
23 < 7 5x 7 7 30 < 5x 30 < 5x 5 5 Whenever, you multiply or divide by a NEGATIVE number change the direction of the inequality symbol. 6 > x x is less than than 6 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Oct 21 11:30 AM 10
EXAMPLE 5 Solve the inequality, then graph the solution set on a number line. SOLUTION Eliminate the fractions by multiplying the entire equation by the least common denominator. Least common denominator of 4, 14, and 7 is 28. 28( ) Oct 21 11:37 AM 11
28( ) 28 28 28 7 2 4 28 28 28 Oct 21 11:41 AM 12
+4x + 4x +21 +21 Oct 21 12:01 PM 13
Keep the direction of the inequality symbol the same, we divided by a positive number. It does matter that the solution is negative number. 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Oct 21 12:03 PM 14
EXAMPLE 6 Solve the inequality, then graph the solution set on a number line. SOLUTION 1 + x + x Oct 21 1:28 PM 15
The inequality is TRUE. ALL REAL NUMBERS 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Sep 7 10:14 PM 16
EXAMPLE 7 Solve the inequality, then graph the solution set on a number line. SOLUTION 6x 6x Oct 21 1:35 PM 17
The inequality is FALSE. NO SOLUTION 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Oct 21 1:39 PM 18
COMPOUND INEQUALITIES Sep 13 12:44 PM 19
EXAMPLE 8 Solve the inequality, then graph the solution set on a number line. SOLUTION Oct 21 1:42 PM 20
Oct 21 1:44 PM 21
How to graph a compound inequality? Rewrite as 2 separate inequalities. AND Sep 7 10:33 PM 22
Graph each inequality separately. 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Oct 21 1:40 PM 23
When graphing compound inequalities with an AND, we will take the INTERSECTION of the graphs. 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Sep 13 2:08 PM 24
EXAMPLE 9 Solve the inequality, then graph the solution set on a number line. 4x + 3 6x >11 OR 4 (3x 5) 12 SOLUTION 4x + 3 6x >11OR 4 1(3x 5) 12 2x + 3<11 3 3 2x < 8 OR 4 1(3x 5) 12 4 3x + 5 12 OR 9 3x 12 Oct 21 2:18 PM 25
2x 8 2 > OR 9 3x 12 9 9 3x 3 2 x < 4 x is less than 4 3x 3 3 3 x 1 x is greather than or equal to 1 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Oct 21 1:55 PM 26
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