Lesson 8.1

 

Objective:  To review the process of solving equation and   word problems.

                     To graph linear equation and parabolas.

TERMS:

Algebraic equation                              4x – 5 = 27

Open sentence

Numerical statement   If x = 3,  becomes 4(3) – 5 = 27 false

False sentence

True sentence

Solving an algebraic equation-process of finding the number or numbers that make a true numerical statement.

Solutions or roots

Solution set

Equivalent equations

 

Property 8.1      Properties of Equality

For all real numbers a, b, and c:

 

  1.  a = a.     Reflexive Property

2.  If a = b, then b = a.    Symmetric Property

  1.  If a = b and b = c, then a = c.  Transitive Property
  2.  If a = b, then a may be replaced by b, or b may be replaced by a, in any statement without changing the meaning of the statement.    Substitution Property.
  3.   a = b iff a + c = b + c          Addition Property
  4.   a = b iff ac = bc, where c 0.  Multiplication Property

 

Solve and give the solution set:       

1.  –4x – 1 = 11

 

 

 

                                               

                               

                                                                                                check

 

solution set

 

  1. a – 2 – 3a = 2a + 1 – 5a

 

 

 

 

                                                                                                                check

 

 

solution set

 

  1. 5( x – 1 ) – 4( x + 2) = -3( x – 1) + 3x + 5

 

 

 

 

 

solution set

4. 

 

 

 

 

 

 

 

 

solution set

 

  1.  0.04x + 0.06( 1200 –x ) = 66

 

 

 

 

 

 

 

 

solution set

6.                 Proportion     iff ad = bc 

             b  0 c  0.

 

 

 

solution set

Algebraic identity                                2x + 1 = 2x + 1

                                                                 x2 – 4x – 12 = ( x – 6 )( x + 2)

 

Solve:     3( x – 1) + 2( x + 4) = 5( x + 1)

 

 

 

 

 

 

 

{ x ! x is a real number}

 

No solution        2x – 3 = 2x + 8

                            5( x – 2) = 5x + 8

 

Solve:   4( a – 2) – 2( a + 3) = 2( a + 6)

 

 

 

 

 

 

 

CW Worksheet #1-6

 

Problem Solving

If $2000 is invested at 8% interest, how much additional money must be invested at 11% interest so the total return for both investments averages 10%?

 

 

 

 

 

 

 

 

 

 

 

 

 

Find three consecutive even integers whose sum is 168.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CW Worksheet #13-15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Graph each equation by plotting points.

 

1.  y = 3x + 2       x   y      Linear equation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.  y = 3x2                                               x   y      parabola

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CW Worksheet #16-18

HW page 310 # 1-25 odd and 37-52 all omitting #48

Page 535 #25-31 odd and 37