Post on 27-Mar-2015
transcript
Compound Inequalities
Objective: To solve conjunctions and disjunctions
Conjunction
• A sentence formed by joining two sentences with the word and.
• x > -3 and x < 4 in order for a value of x to make the statement true both conditions must be satisfied.
-3 4
Disjunction
• Formed by joining two sentences with the word or
• A solution only has to satisfy one of the conditions to be true
• x > 2 states that x > 2 or x = 2, notice that the dot is shaded in to show equality.
• x > 3 or x < 12
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Solving Inequalities With Disjunction
• 2x + 3 < 7 or -4x < -16• 2x + 3 – 3 < 7 – 3 • 2x < 4• 2x/2 < 4/2• x < 2
• -4x < -16• -4x/-4 > -16/-4• x > 4
x < 2 or x > 4
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Solving Inequalities With Conjunction
• 4 < 2(x – 1)• 4 < 2x – 2 distribute• 4 + 2 < 2x – 2 + 2• 6 < 2x• 6/2 < 2x/2• 3 < x• x > 3
• 2(x – 1) < 8• 2x – 2 < 8 distribute• 2x – 2 + 2 < 8 + 2• 2x < 10• 2x/2 < 10/2• x < 5
4 < 2(x – 1) < 84 < 2(x – 1) and 2(x – 1) < 8
x > 3 and x < 5
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Alternative Solution For Conjunction
• 4 < 2(x – 1) < 8
• 4 < 2x – 2 < 8 distribute
• 4 + 2 < 2x – 2 + 2 < 8 + 2
• 6 < 2x < 10
• 6/2 < 2x/2 < 10/2
• 3 < x < 5
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Try These! Solve and Graph each Compound Inequality
• -2 < 3x + 1 or 3x < -9
• 6 < 3x + 6 < 12
• 6 > 2x > -8
• 2x – 1 > 3 or x – 2 < 3
• 2x + 3 < 3 and x – 4 > 1
• x > -1 or x < -3• Click for solution• 0 < x < 2• Click for solution• -4 < x < 3• Click for solution• All Real Numbers• Click for solution• Ø• Click for solution
-1-3
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3-4
End show
-2 < 3x + 1 or 3x < -9
• -2 – 1 < 3x + 1 – 1 • -3 < 3x • -3/3 < 3x/3• -1 < x• x > -1
• 3x/3 < -9/3• x < -3
• x > -1 or x < -3
Back to Try These!
6 < 3x + 6 < 12
• 6 – 6 < 3x + 6 – 6 < 12 – 6
• 0 < 3x < 6
• 0/3 < 3x/3 < 6/3
• 0 < x < 2
Back to Try These!
6 > 2x > -8
• 6/2 > 2x/2 > -8/2
• 3 > x > -4
• -4 < x < 3
Back to Try These!
2x – 1 > 3 or x – 2 < 3
• 2x – 1 + 1 > 3 + 1• 2x > 4• 2x/2 > 4/2• x > 2
• x – 2 + 2 < 3 + 2• x < 5
• x > 2 or x < 5
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Back to Try These!
2x + 3 < 3 and x – 4 > 1
• 2x + 3 – 3 < 3 – 3 • 2x < 0• 2x/2 < 0/2• x < 0
• x – 4 + 4 > 1 + 4• x > 5
• Because there is no value for x that satisfies x < 0 and x > 5 simultaneously there is no solution for the inequality
Back to Try These!