Solving Inequalities

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Solving Inequalities

• More or Less

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Music, music, music . . .

• Aaron can afford to spend 50 to buy some concert
  tickets at 18 each and pay for parking at 5.
  How many tickets can he buy?
• He borrows 50 from his mom for the concert. He
  repays the loan at the rate of 6 per week. When
  will his debt be under 20?

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7.1 Addition and Subtraction Properties of
Inequalities

• For all numbers a, b, and c, the following are
  true
• 1. If a gt b, then a c gt b c
• and a c gt b c
• 2. If a lt b, then a c lt b c
• and a c lt b c
• That is, the inequality stays the same when you
  add or subtract the same positive number or
  negative number from both sides of the inequality.

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7.2 Multiplication and Division Properties of
Inequalities

• For all numbers a, b, and c, the following are
  true
• 1. If c is positive and a gt b, then ac gt bc
• and a/c gt b/c and if c is positive and
• a lt b, then ac lt bc and a/c lt b/c
• 2. If c is negative and a lt b, then ac gt bc
• and a/c gt b/c, and if c is negative and
• a gt b, then ac lt bc and a/c lt b/c.

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In simpler terms

• An inequality stays the same if you multiply or
  divide both sides of an inequality by the same
  positive number.
• An inequality is reversed if you multiply or
  divide both sides of an inequality by the same
  negative number.

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Solve each inequality and graph the solution set

• a/4 gt 16
• - 15 lt x/3
• t 9 lt 6
• 2y 10 y 6
• 0.9 p - 3.4
• - 9v lt -108

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Define a variable and write an inequality

1. Four times a number is at most 36.
2. The opposite of three times a number is less than
   36.
3. A number decreased by 4 is at least 9.
4. 80 of a number is less than 24.

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7.3 Solving Multi-Step Inequalities

• 3(x 2) 8x lt 44
• 7x 1 lt 29 2x
• 3x 4 gt 2(x3) x

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Assignment

• 7.3 21 41 odds, 46-48, 51,54,55