# solving one-step inequalities 763542 8. objective: to solve one-step inequalities using properties...

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Solving One-Step Solving One-Step Inequalities Inequalities 7 6 3 5 4 2 8 12 7 > + x 12 7 > + x

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Solving One-Step Solving One-Step InequalitiesInequalities

763 542 8

127 >+x 127 >+x

Objective: To solve one-step inequalities using

properties for inequalities

Solving One-Step Solving One-Step InequalitiesInequalities

Solving One-Step Solving One-Step InequalitiesInequalities

What are the Properties for Inequalities?

Are they the same as for regular equations?

Solving One-Step InequalitiesSolving One-Step Inequalities

X-15<73 X-

15+15<73+15X<88

Solving One-Step InequalitiesSolving One-Step Inequalities

Subtraction Property for Inequalities

y+15<25 Y+15-15<25-

15 y<10

Subtract 15 from both sides

Solving One-Step InequalitiesSolving One-Step Inequalities

Multiplication Property for Inequalities

105

=x

5105

5 ×=×x

50=xMultiply both sides by the reciprocal of the coefficient

Solving One-Step InequalitiesSolving One-Step Inequalities

Division Property for Inequalities

205 >x

5

20

5

5>

x

4>x

Divide both sides by the coefficient of x

Division Property for Inequalities Caution! Dividing

by a negative number205 <− x

5

20

5

5

−<

−− x

4−>x

Notice: Sign CHANGED

Same if multiplying?

Multiplication Property for Inequalities

Caution! When you multiply by a negative number…

…the sign CHANGES

YES!-x > 2

5

(-5 )-x > 2(-5) 1 5

x < -10

Solving One-Step Solving One-Step InequalitiesInequalities

Let’s try some on our own …… ready?

Solving One-Step Solving One-Step InequalitiesInequalities

76 ≤+x 1

Solving One-Step Solving One-Step InequalitiesInequalities

53 −≤x 2

Solving One-Step Solving One-Step InequalitiesInequalities

153 −≥− x 3

Solving One-Step Solving One-Step InequalitiesInequalities

59 −>−x 4

1.1.x ≤ x ≤ 112.2. 8 ≤ x or x ≥ 88 ≤ x or x ≥ 8

3.3. x ≤ 5x ≤ 5

4.4. x > 4x > 4

Solving One-Step Solving One-Step InequalitiesInequalities

32

1−≥x

5

Solving One-Step Solving One-Step InequalitiesInequalities

73

−>−

x 6

Solving One-Step Solving One-Step InequalitiesInequalities

75 ≥+ x 7

Solving One-Step Solving One-Step InequalitiesInequalities

53

>x 8

5.5. x ≥ -6 x ≥ -6

6.6. 21 < x or x > 21 21 < x or x > 21

7.7. x ≥ 2 x ≥ 2

8. 8. x > 15x > 15

Please take out a Please take out a piece of paper and piece of paper and write down what the write down what the steps are for solving steps are for solving a one-step inequalitya one-step inequality

Reflection

Solving One-Step Inequalities

Excellent Job !!! Well Done