Solving Linear Equations
Objective: Identify and solve equations that are linear in nature.
Title: Jul 31 ­ 2:11 PM (1 of 10)
Linear equations are equations such as
3x + 12 = 0,
0.62x ­ 0.3 = 0
Sometimes a linear equation is called a first­degree equation, because the variable is of degree 1.
Title: Jul 31 ­ 2:11 PM (2 of 10)
Solve the equation: 3(x ­ 2) = 5(x ­ 1)
3x ­ 6 = 5x ­ 5
3x = 5x + 1
­2x = 1
x = Title: Jul 31 ­ 2:11 PM (3 of 10)
­1
2
Notation
The book uses brackets to show a finite set of solutions. This is called set notation.
If
Title: Jul 31 ­ 2:11 PM (4 of 10)
the book will say, "The solution set is "
Solve The solution set is Title: Jul 31 ­ 2:11 PM (5 of 10)
Solve
9x ­ (7x ­ 1) = 2
9x ­7x + 1 = 2
2x + 1 = 2
2x = 1
1
2
{ }
Title: Jul 31 ­ 2:11 PM (6 of 10)
Solve
2x
= 2 + 1 x
5
3
2x
5
1 x
3 = 2
6
x
15
5 x
= 2
15
1
x = 2
15
1
.
x = 2 . 15
15
15
{30}
Title: Jul 31 ­ 2:11 PM (7 of 10)
Solve
2x
= 2 + 1 x using another method.
5
3
Find the least common denominator (LCD) for the fractions in the problem, then multiply every term by the LCD.
Title: Jul 31 ­ 2:11 PM (8 of 10)
The LCD in this example is 15.
15 . 15 . 13 x
15 . 52 x = 2 + 6x = 30 + 5x
x = 30
{30}
Title: Jul 31 ­ 2:11 PM (9 of 10)
Homework:
pg. 998
#'s: 13­30
Title: Jul 31 ­ 2:11 PM (10 of 10)