 # SOLVING MULTI-STEP INEQUALITIES TWO STEP INEQUALITIES Solve: 2x – 3 < 13 +3 Verbal Expressions for = 2x < 16 2 2 x < 8 CHECK!

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SOLVING MULTI-STEP INEQUALITIES TWO STEP INEQUALITIES Solve: 2x – 3 < 13 +3 Verbal Expressions for = 2x < 16 2 2 x < 8 CHECK!

SOLVING MULTI-STEP INEQUALITIES TWO STEP INEQUALITIES Solve: 5 – 3x < 20 -5 Verbal Expressions for = -3x < 15 -3 -3 x > - 5 CHECK! DING!

SOLVING MULTI-STEP INEQUALITIES Solve: 5(x – 3) + 2 < 12 +13 Verbal Expressions for = 5x < 25 5 5 x < 5 CHECK! 5x – 15 + 2 < 12 5x – 13 < 12

SOLVING MULTI-STEP INEQUALITIES Solve: 5 + 3(7 – x) > 32 -26 Verbal Expressions for = -3x > 6 -3 -3 x < -2 CHECK! 5 + 21 – 3x > 32 26 – 3x > 32 DING!

SOLVING COMPOUND INEQUALITIES Graph the solution sets for: x 7 x > 2 and x < 7 x > 2 or x < 7 2 7 2 7 NO SOLUTION 2 7 2 7 ALL REALS

SOLVING COMPOUND INEQUALITIES A compound inequality containing “and” is true only if both inequalities are true. So, the graph of a compound inequality containing “and” is the INTERSECTION of the graphs of the two inequalities.

SOLVING COMPOUND INEQUALITIES Solve and graph the solution set: x + 5 > 2 and x - 3 < 7 -5 -5 x > -3 and x < 10 +3 +3 -3 10

SOLVING COMPOUND INEQUALITIES Solve and graph the solution set: 6 < x + 2 < 12 4 10 -2 -2 -2 4 < x < 10

SOLVING COMPOUND INEQUALITIES A compound inequality containing “or” is true only if one or more of the inequalities is true. So, the graph of a compound inequality containing “or” is the UNION of the graphs of the two inequalities.

SOLVING COMPOUND INEQUALITIES Solve and graph the solution set: 2x – 3 < 7 or 3 – x < -8 5 11 +3 +3 2x < 10or -3 -3 -x < -11 2 2 x < 5or -1 -1 x > 11 DING!

SOLVING COMPOUND INEQUALITIES Try These: Solve and graph the solution set: 10 < x + 3 < 22 -3 -3 -3 7 < x < 19 7 19

SOLVING COMPOUND INEQUALITIES Try These: Solve and graph the solution set: 2x + 3 < 9 or 5 – x < -2 -3 -3 2x < 6 2 2 x < 3 or -5 -5 -x < -7 -1 -1 “ding” or x > 7 3 7

SOLVING COMPOUND INEQUALITIES Try These: Solve and graph the solution set: x + 6 > 2 and x - 8 < 7 -6 -6 x > - 4and +8 +8 x < 15 - 4- 4 15

SOLVING COMPOUND INEQUALITIES Try These: Solve and graph the solution set: 3x > 9 or x + 6 < 7 3 3 x > 3 or -6 -6 x < 1 1 3

SOLVING COMPOUND INEQUALITIES Working backwards: Write the compound inequality for the following graphs: 0 246-2 -4 -6 x > -2 and x < 4 OR -2 < x < 4

SOLVING COMPOUND INEQUALITIES Working backwards: Write the compound inequality for the following graphs: 0 246-2 -4 -6 x 3

SOLVING COMPOUND INEQUALITIES Working backwards: Write the compound inequality for the following graphs: 0 246-2 -4 -6 -2 < x < 4 x > -2 and x < 4

SOLVING COMPOUND INEQUALITIES Working backwards: Write the compound inequality for the following graphs: 0 246-2 -4 -6 x 4

SOLVING COMPOUND INEQUALITIES Working backwards: Write the compound inequality for the following graphs: 0 246-2 -4 -6 0 < x < 1 x > 0 and x < 1

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