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					    Today’s Lesson


Solving Multistep
Linear Inequalities
Unit 3-Lesson 10
    Warm-Up Activity


Let’s warm up today by
practicing our algebra skills
with partners.
The sum of 3 and 40 percent of a
number is equal to 15.
What is the number?
Let x = a number   40% = 0.4
 3 + 0.4x = 15     to “undo” a positive you
                      must use a negative
–3          –3
                     What you do to one side of
   0.4 x = 12       the equation, be sure and do
                            to the other.
Let x = a number
 3 + 0.4 x = 15
–3          –3
     0.4 x = 12       to “undo”
                   multiplication you
     0.4 0.4         must divide

                   What you do to one side
      x = 30       of the equation, be sure
                     and do to the other.
The difference of 20 percent of a
number and 10 is equal to 90.
What is the number?
Let x = a number     20% = 0.2
  0.2x –10 = 90    to “undo” subtraction you
                           must add
       +10 +10
                       What you do to one side
   0.2 x = 100         of the equation, be sure
                         and do to the other.
Let x = a number

   0.2x –10 = 90
       +10 +10
    0.2 x = 100    to “undo” multiplication
                        you must divide
     0.2 0.2
                   What you do to one side
     x = 500       of the equation, be sure
                     and do to the other.
Leo owns a small thrift shop where
the daily revenue averages $650.

What can his costs be if he wants
a profit of at least $525 per day?
 Let x = costs
650 – x ≥ 525
–650      –650      to “undo” a positive you
                       must use a negative

       –x ≥ –125   When you multiply or divide
                   both sides of an inequality by
       –1     –1      a negative number, the
       x ≤ 125      direction of the inequality
                         must be changed.

  The costs must remain below $125.
Whole-Class Skills Lesson

Today we will be solving
multistep linear equations.
• When solving one-step inequalities,
  the steps are the same as the steps for
  solving one-step equations.

• The only important difference is paying
  added attention to reversing the
  inequality if you multiply or divide
  both sides by a negative value.
• The same is true for multistep
  inequalities.
           Solve for x.
–3(2x – 4) + 2x – 5 < –13
–6x + 12 + 2x – 5 < –13 distribute the –3
          –4x + 7 < –13     collect like terms
                            subtract 7 from
               –7    –7       both sides
            –4x < –20        divide by –4
             –4    –4       reverse the
                x>5         inequality
               Solve for x.
         4
           x – 8 < 24
         5
               +8       +8       add 8 to both sides

     5 4        5        multiply by the
     x < 32    
     4 5        4         reciprocal

               x < 40
        
    Solve for x.
–3x + 1 ≥ 42   exponent first
–3x + 1 ≥ 16
               subtract 1 from
    –1 –1        both sides
  –3x ≥ 15
  –3 –3            divide by –3

                reverse the
    x ≤ –5      inequality
      Solve for x.
4 + 5x – 6x < 32
                    exponent first
4 + 5x – 6x < 9
                   collect like terms
   4–x<9
                   subtract 4 from
   –4  –4
                     both sides
      –x < 5
                   divide by –1
     –1 –1
                    reverse the
      x > –5        inequality
      Solve for x.
3(4x + 5) ≤ 75
                     distribute the 3
12x + 15 ≤ 75
                    subtract 15
   –15 –15        from both sides

    12x ≤ 60     divide by 12
    12 12

      x≤5

				
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