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 Words Is 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 > ≤ 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 > -8.1 You must switch the inequality!!! -9 -9 x < 0.9

Example 2 Graph y < -2 -3 -2 -1 Steps to Solve and Graph Solve inequality (hear the bell when needed) Make number line to include solution (usually 3 to 4 numbers is all you need) Put circle on solution then decide if open or closed Read inequality to decide which way to shade (less than letter left: greater than letter right) 5) Check solution Example 2 Graph y < -2 -3 -2 -1 Do not write steps Done 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 4 5 6 Do not need to write all steps Done 4 5 6 Do not need to write all steps Done 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

Example 4: Solve and Graph 1) Move variables to left constants to right Hear the bell? 0 1 2 3 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? [ , ∞)

Assignment 2-4 /77 /1-39 odd, 46-51 (on 8-39 solve and graph)