A.5 Day 1 ­ Solving Linear Equations
August 26, 2008
Solving Linear Equations
Objective: Identify and solve equations that are linear in nature.
Jul 31 ­ 2:11 PM
1
A.5 Day 1 ­ Solving Linear Equations
August 26, 2008
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.
Jul 31 ­ 2:11 PM
2
A.5 Day 1 ­ Solving Linear Equations
August 26, 2008
Solve the equation: 3(x ­ 2) = 5(x ­ 1)
3x ­ 6 = 5x ­ 5
3x = 5x + 1
­2x = 1
x = ­1
2
Jul 31 ­ 2:11 PM
3
A.5 Day 1 ­ Solving Linear Equations
August 26, 2008
Notation
The book uses brackets to show a finite set of solutions. This is called set notation.
If
the book will say, "The solution set is "
Jul 31 ­ 2:11 PM
4
A.5 Day 1 ­ Solving Linear Equations
August 26, 2008
Solve The solution set is Jul 31 ­ 2:11 PM
5
A.5 Day 1 ­ Solving Linear Equations
Solve
August 26, 2008
9x ­ (7x ­ 1) = 2
9x ­7x + 1 = 2
2x + 1 = 2
2x = 1
1
{ }
2
Jul 31 ­ 2:11 PM
6
A.5 Day 1 ­ Solving Linear Equations
Solve
August 26, 2008
2x
= 2 + 1 x
5
3
2x
5
1 x
3 = 2
6
x
15
5 x
= 2
15
1 x
= 2
15
15 . 1 x = 2 . 15
15
{30}
Jul 31 ­ 2:11 PM
7
A.5 Day 1 ­ Solving Linear Equations
Solve
August 26, 2008
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.
Jul 31 ­ 2:11 PM
8
A.5 Day 1 ­ Solving Linear Equations
August 26, 2008
The LCD in this example is 15.
2x
= 2 + 1 x
5
3
15 . 15 . 13 x
15 . 52 x = 2 + 6x = 30 + 5x
x = 30
{30}
Jul 31 ­ 2:11 PM
9
A.5 Day 1 ­ Solving Linear Equations
August 26, 2008
Homework:
pg. 998
#'s: 13­30
Jul 31 ­ 2:11 PM
10