Lesson 2-4: Solving Inequalities Objective Students will solve and graph inequalities using addition/subtraction/multiplication/division and check that a number is a solution.

Inequalities WordsIs less than Is greater than Is less than or equal to OR at Most Is greater than or equal to OR is at least Symbols On number line < Open circle > Open circle ≤ Closed circle ≥ Closed circle

Interval Notation [ or ] Boundary number is included ( or ) Boundary number is not included Write interval notation for the following: x > 3 (3, ∞) w ≤ -2 (- ∞,-2]

Solve inequalities like equations except… If you multiply or divide an inequality by a negative, switch the inequality symbol. Example 1 -9x > You must switch the inequality!!! x < 0.9

Steps to Solve and Graph 1)Solve inequality (hear the bell when needed) 2)Make number line to include solution (usually 3 to 4 numbers is all you need) 3)Put circle on solution then decide if open or closed 4)Read inequality to decide which way to shade (less than letter left: greater than letter right) 5) Check solution Example 2 Graph y < -2 Do not write steps Done 2) Solution in center 1 or 2 numbers on each side 3) -2 is boundary and equal so circle is closed 4) Read y is less than or equal to -2 so line is to left 5) Pick a point line goes through see if it is true -6 ≤ -2 so yes

Example 3 Graph 5 > x Do not need to write all steps Done 2) Solution in center 1 -2 numbers on each side 3) 5 is boundary and not equal so circle is open 4) Read 5 is greater than x so…. x is less than five so shade line to left 5) Pick a point line goes through see if it is true 5 > -1 so yes 4 5 6

Example 4: Solve and Graph Move variables to left constants to right Hear the bell? 1) 2) Solution in center 1 -2 numbers on each side (between 1 and 2) 3) More than 1.5 and equal so circle is closed 4) Read y is greater than so shade to right 5) Pick a point line goes through see if it is true 10 > so yes What is the solution in interval notation? [, ∞)

Marker Boards pg

Assignment 2-4 /77 /1-39 eoo, (on 9-39 solve, interval notation and graph)