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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Presentation transcript:

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

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

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

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

SOLVING COMPOUND INEQUALITIES Graph the solution sets for: x 7 x > 2 and x < 7 x > 2 or x < NO SOLUTION 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 < x > -3 and x <

SOLVING COMPOUND INEQUALITIES Solve and graph the solution set: 6 < x + 2 < < 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 < x < 10or x < x < 5or x > 11 DING!

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

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

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

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

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

SOLVING COMPOUND INEQUALITIES Working backwards: Write the compound inequality for the following graphs: x 3

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

SOLVING COMPOUND INEQUALITIES Working backwards: Write the compound inequality for the following graphs: x 4

SOLVING COMPOUND INEQUALITIES Working backwards: Write the compound inequality for the following graphs: < x < 1 x > 0 and x < 1