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Solving Inequalities

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					Solving Inequalities
      Lesson 24
                 EXAMPLE 1
                  X-2.7>1.3
   STRATEGY: Isolate the variable x.
   STEP 1: Add 2.7 to both sides.
             x-2.7+2.7>1.3+2.7
                   x>4
   STEP 2: Check the answer by selecting a few
    numbers.      5-2.7>1.3 OR 4.1-2.7>1.3
                   2.3>1.3             1.4>1.3

   SOLUTION: All numbers greater than 4.
                  EXAMPLE 2
                   4z +3 ≤ -5
   STRATEGY: Isolate the variable z.
   STEP 1: Subtract 3 from both sides.
                    4z+3-3 ≤ -5-3
                    4z ≤-8
   STEP 2: Divide both sides by 4. 4z/4 ≤-8/4
                                        z ≤-2
   STEP 3: Check. 4(-3) +3 ≤-5
                    -12+3 ≤-5
                      -9 ≤-5
   SOLUTION: Numbers greater than or equal to -2.
     1. 3 + x > 10
A x<7     The   answer
B x>7      is…
C x<13       B
D x>13
     2. 2y ≥ 32
A y≤64   The   answer
B y≥30    is…
C y≥16       C
D y≤8
      3.     3z ≤ 4.2
A z ≤ 7.2     The   answer
B z< 1.4       is…
C z ≤ 1.4        C
D z > 1.4
     4. v/5 + 20 > 30
A v>2       The   answer
B v<50       is…
C v>50             C
D v<550
     5. 10q < 150
A q>15    The   answer
B q<15     is…
C q>140          B
D q<140
     6. 2k/5 ≥ 10
A k<2     The   answer
B k ≥5     is…
C k≤15           D
D k ≥25
     7. f+2.1>3
A f<0.9   The   answer
B f>0.9   is…
C f<5.1          B
D f<5.1
      8. 2p ≤ 1
A p≤½     The answer
B p ≤ 2   is…
C p ≥ ½          A
D p ≥ 2
 9. Joel decides to collect baseball cards.
He buys 8 cards each week. He wants to
  have at least 40 cards in his collection.
  This inequality can be used to find the
number of weeks it will take him to reach
 his goal. The variable w represents the
        number of weeks. 8w≥40


 A.   8w/8 ≥ 40/8
          w≥5

				
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