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Chapter 2
Discovery 1
Linear Equations with Noninteger Solutions
(5 x  4)  2(3x  1)  2( x  7) does not have an integer solution.
Complete the table of values, compare the values obtained, and
determine their differences.
x
3
(5 x  4)  2(3x  1)  2( x  7)
8
1
1  8
1  (8)  7
4
5
6
7
Write a rule for determining when the solution of an equation is
between two integers given in a table of values.
Chapter 2
Discovery 2
Linear Equations with No Solution
1. Solve 2 x  5  2 x  10 numerically by completing a table
of values.
Write a rule explaining how to solve the equation by
viewing its table of values.
2. Solve 2 x  5  2 x  10 graphically. Sketch the graph.
Write a rule explaining how to solve the equation by
viewing its graph.
Chapter 2
Discovery 3
Linear Equation with Many Solutions
1. Solve 2 x  5  ( x  3)  ( x  2) numerically by completing
a table of values.
Write a rule explaining how to solve the equation by viewing
its table of values.
2. Solve 2 x  5  ( x  3)  ( x  2) graphically. Sketch the graph.
Write a rule explaining how to solve the equation by viewing
its graph.
Chapter 2
Discovery 4
Linear Equation with No Solutions
Solve algebraically the previous example of a linear
equation with no solution:
2 x  5  2 x  10
Write a rule that explains why the equation has no
solution.
Chapter 2
Discovery 5
Linear Equation with Many Solutions
Solve algebraically the previous example of a linear
equation with many solutions: 2x + 5 = (x + 3) + (x + 2).
Write a rule that explains why the equation has many
solutions.
Chapter 2
Discovery 6
Solving a Linear Absolute-Value Equation
Solve each equation graphically and check your
solution numerically.
1. a.
x4 3
2. a.
x  4  3
3. a.
x4 0
b.
3 x  2
b.
3  x  2
b.
x 3  0
Write a rule that gives the number of solutions of a linear
absolute-value equation when the absolute-value
expression equals a positive number, a negative number,
and 0.