Solving Compound Inequalities And Rule 1: Whatever you do to one section you have to do to the other two. Rule 2: Remember all of the rules for solving equations. Rule 3: If you multiply/divide by a negative number you must change the direction of the inequality symbol.

-2 < x < 3 AND -2 < 3x + 4 < 13 -4 -4 -4 -6 < 3x < 9 -4 -4 -4 -6 < 3x < 9 3 3 3 -2 < x < 3

Solving Compound Inequalities OR Rule 1: Work each piece separately. Rule 2: Remember all of the rules for solving equations. Rule 3: If you multiply/divide by a negative number you must change the direction of the inequality symbol.

OR 2x + 3 < 5 or 4x – 7 > 9 -3 -3 +7 +7 2x < 2 or 4x > 16 2 2 4 4 x < 1 or x > 4

Solving Absolute Value Equations and Inequalities Sect 1.7 Solving Absolute Value Equations and Inequalities

The result of an absolute value is always positive. of a number x, written |x|, is the distance a number is form 0 on the number line. The result of an absolute value is always positive.

Examples: |-5| = 5 |5| = 5 Your turn to try: |-2| = 2 |2| = 2

To Solve an absolute value equation of the form |x| = c, where c > 0, you must consider 2 answers: x = c or x = -c

Examples: |x| = 5 x = 5 or x = -5 |x| = -2 -2 No solution Remember: an Absolute Value result is always positive

Solving Absolute Value Equations |ax + b| = c, where c > 0 is equivalent to the compound statement: ax + b = c or ax + b = -c

Steps for solving Absolute value equations: Step 1: Rewrite problem as the compound or statement Step 2: Solve each new equation separately Step 3: Write the answer

Examples: |2x – 5| = 9 Step 1: Rewrite 2x – 5 = 9 or 2x – 5 = -9

Step 2: Solve individually 2x – 5 = 9 or 2x – 5 = -9 +5 +5 +5 +5 2x = 14 or 2x = -4 2 2 2 2 Step 3: Write answer x = 7 or x = -2

Your Turn Again: |3x + 8| = 20 3x + 8 = 20 or 3x + 8 = -20 -8 -8 -8 -8 -8 -8 -8 -8 3x = 12 3x = -28 3 3 3 3 x = 4 or x = -28/3

Solving Absolute Value Inequalities |ax + b| < c, where c > 0 is equivalent to the compound statement: -c < ax + b < c

Solving Absolute Value Inequalities |ax + b| > c, where c > 0 is equivalent to the compound statement: ax + b > c or ax + b < -c

Recap: Absolute value equations and inequalities are both solved with compound statements. >, ≥, = are all or statements <, ≤ are and statements

Your turn once again: -9 < x < 2 |2x + 7| < 11 -7 -7 -7 -18 < 2x < 4 2 2 2 -9 < x < 2

Now try this one: x ≥ 10/3 or x ≤ -2 |3x - 2| ≥ 8 +2 +2 +2 +2 3x ≥ 10 or 3x ≤ -6 3 3 3 3 x ≥ 10/3 or x ≤ -2

Classwork – Journal entry – What are the steps for solving compound inequalities and absolute values? Pg 53 1, 2, 4, 7, 10, 13 Homework – Pg 46 39, 40, 43, 44 Pg 53 – 54 17-44 every 3rd, 47-50