L1-5 Algebra 2

L1-5 Obj: Solve equations and inequalities involving absolute value Distance from zero Distance is positive Example: Give all solutions to the equations x = 7 or x = -7 no solution x = 0

Solve |15 – 3x| = 6. Absolute Value Equations and Inequalities LESSON 1-5 Additional Examples Solve |15 – 3x| = 6.

Steps for solving absolute value equations Isolate the absolute value Rewrite the equation as two separate equations, one equal to the number, one equal to the opposite of the number Solve each equation Check your answers

Solve 4 – 2|x + 9| = –5. Absolute Value Equations and Inequalities LESSON 1-5 Additional Examples Solve 4 – 2|x + 9| = –5.

Solve |3x – 4| = –4x – 1. Absolute Value Equations and Inequalities LESSON 1-5 Additional Examples Solve |3x – 4| = –4x – 1.

Absolute Value Distance from zero Abs > number means the distance from zero is great. Abs < number means the distance from zero is small.

Additional steps for solving absolute value inequalities If abs > number, write two inequalities with “or” in the middle The first is the same without the bars The second change the inequality and the sign of the other number If abs < number, write a single inequality Put the expression in the bars in the middle Opposite of number < expression < number

Solve |2x – 5| > 3. Graph the solution. Absolute Value Equations and Inequalities LESSON 1-5 Additional Examples Solve |2x – 5| > 3. Graph the solution.

Solve –2|x + 1| + 5 –3. Graph the solution. > – Absolute Value Equations and Inequalities LESSON 1-5 Additional Examples Solve –2|x + 1| + 5 –3. Graph the solution. > –

Absolute Value Equations and Inequalities LESSON 1-5 Additional Examples The area A in square inches of a square photo is required to satisfy 8.5 A 8.9. Write this requirement as an absolute value inequality. < – < –

Practice Solve (check for extraneous answers) |2x-3|=4x-1 Solve and graph |x-5|>8 Write an absolute value inequality 50<k<51 Homework: L1.5 (p 36) #8-38, 44-50e