Lesson 6.3- Solving Multi-Step Inequalities, pg. 332

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Lesson 6.3- Solving Multi-Step Inequalities, pg.
332

• Goals To solve linear inequalities involving
  more than one operation.
• To solve linear inequalities involving the
  Distributive Property.

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Steps for Solving Linear Inequalities

• Remove fractions
• - Multiply by the LCD.
• Simplify
• - Remove parentheses using the
  distributive property
• - Combine like terms
• Undo addition/subtraction
• - Get the variables on one side of the
  inequality sign
• - Get the numbers without variables on
  the other side of
• the inequality sign.
• Simplify the expressions on each side of the
  inequality sign.
• Undo multiplication/division

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Ex. 1 Solve each inequality.

• 1. 13 11d 79

• 2. -4y 23 lt 19

4

• 3.

• 4. 7b 11 gt 9b - 13

5

• 5. -5(g 4) gt 3(g 4)

• 6. 3 5t 3(t 1) 4(2 t)

6

• 7. -3m 6 -3

• 8.

7

• 9. 3y 4 gt 2(y 3)

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• 10. 4(y 1) 3(y 5) 3(y 1)

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Your turn..

• 11. 7q 1 2q 29

• 12. 9r 15 24 10r

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• 13.

• 14.

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Ex. 2 Define a variable, write an inequality,
and solve each problem.

• One-eighth of a number decreased by five is at
  least thirty.
• Negative four times a number plus nine is no more
  than the number minus twenty-one.

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3. Seven minus two times a number is less than
three times the number plus thirty-two.
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Summary

• Use the same steps to solve a linear inequality
  that you used to solve linear equations
• When MULTIPLYING and DIVIDING both sides of an
  inequality by a NEGATIVE number, REVERSE the
  INEQUALITY SYMBOL.
• NBA 9, page 335, problems 16-38 even