Download Section 2.1 Solving Linear Equations Part I: Addition Property of

Section 2.1
Solving Linear Equations Part I: Addition Property of Equality
What is a Linear Equation?
Definitions
A linear equation in one variable can be written in the form
A, B and C , with A  0 .
The solution, or root, of an equation in x is ____________________________________
_______________________________________________________________________.
Equivalent equations are equations that ______________________________________.
Tool #1: Addition Property of Equality
If A, B, and C are real numbers, then the equations A  B and A  C  B  C are
______________________
Example 1: Solve each equation.
a) x  8  9
c)
1
4
x7   x
5
5
b)
y  6  10
d)
x  21.5  13.4
Solving Linear Equations
Example 2: Solve each equation and check your solution
a) 4 x  3x  6  6 x  10  3
b) 8x  3  7 x  1  6
c)  53x  3  1  16 x   0
e)  51  2 x   43  x   73  x   0
d)
6
3 4 1
1
x   x
7
4 5 7
6
Section 2.2
Linear Equations Part II: The Multiplication Property of Equality
Tool #2: Multiplication Property of Equality
If A, B, and C are real numbers, then the equations
are equivalent equations
Example 2: Solve each equation and check your solution
a) 7 x  10
b) 5x  70
c) .9 x  18
d)
1
x  3
5
e) 
5
4
x
6
9
f)  y  
1
2
Ex 2 Solve each equation and check your solution
a) 9 x  2 x  121
b) 11x  5x  6 x  168
c)  5x  4 x  8x  0
d) 10 x  6 x  3x  4