4.1 Solving Inequalities using Addition and Subtraction
Vocabulary:• inequality: a mathematical sentence formed by placing an inequality symbol between two expressions.• graph of an inequality: is the set of points that represent all solutions of the inequality.• equivalent inequalities: inequalities that have the same solution.
Graphing:• x>1 greater than open dot• x<1 less than open dot• x ≤1 less than or equal solid dot• x ≥ 1 greater than or equal solid dot
Example 1:Write and graph an inequality that describes the situation1.)The speed limit on the road is 45 miles per hour.2.) A child must be taller than 40 inches to get on Space Mountain.
Example 2 Write inequalities from graphsWrite an inequality represented by the graph.a.SOLUTIONThe shading includes all numbers to the right of(greater than) – 6.5.ANSWERAn inequality represented by the graph is x > – 6.5.
Example 2 Write inequalities from graphsWrite an inequality represented by the graph.b.SOLUTIONThe shading includes 4 and all numbers to the left of(less than) 4.ANSWERAn inequality represented by the graph is x ≤ 4.
Example 3 Solve an inequality using subtractionSolve 9 ≥ x + 7. Graph your solution. 9 ≥ x +7 Write original inequality. .
Example 3 continueSolve the inequality. Graph your solution. – 2 < y + 15
Try on your own!!Solve the inequality. Graph your solution.7. y + 5 > 6ANSWER y >18. x + 7 ≥ – 4ANSWER x ≥ –11