Solving Absolute Value Inequalities Algebra 2 Unit 1, Lesson 2.3

Solving Absolute Value Inequalities Algebraically Graphically

Solve Algebraically

Solve Algebraically 4−𝑥 +15>21

Solve on your own: 𝑥+1 −10≤−2 Remember to isolate absolute value Separate into two equations and reverse.

Solution 4−𝑥 +15≥21 −12≤𝑥 𝑎𝑛𝑑 𝑥≤4 −12≤𝑥≤4 −12≤𝑥 𝑎𝑛𝑑 𝑥≤4 −12≤𝑥≤4 Why is the format of the solution different?

Practice Pause and solve problems 11, 12, and 13 from lesson 3 in your assignment packet. 11. 2 𝑥− 7 2 +3>4 12. 2𝑥+1 −4<5 13. 3 𝑥+4 +2≥5

Practice Solutions 11. 𝑥<3 𝑜𝑟 𝑥>4 12. −5<𝑥 𝑎𝑛𝑑 𝑥<4 −5<𝑥<4 13. 𝑥≤−5 𝑜𝑟 𝑥≥−3 𝑥<3 𝑜𝑟 𝑥>4

Solving Graphically 𝑥+3 +1>4 Solve the inequality graphically Graph both sides of the equation y= 𝑥+3 +1 𝑦=4

Solving Graphically 𝑥+3 +1>4 Solve the inequality graphically Graph both sides of the equation y= 𝑥+3 +1 𝑦=4 Intervals on the x axis: −6≥𝑥 𝑜𝑟 𝑥≥0

On your Own Solve: 𝑥 −2 −3≤1 Hint: Begin by graphing both sides

On your Own Solve: 𝑥 −2 −3≤1 Final Solution −2≤𝑥≤6 Hint: Begin by graphing both sides Final Solution −2≤𝑥≤6 Why different format?

Final Thoughts When does an absolute value inequality apply to a real-world situation? Remember you can always check your solution but placing a value in for the variable to see if the equation remains true.