Download Variable: a number that you don`t know, often represented by "x" or "y"

Solving Linear Equations
Definitions:
Variable: a number that you don't know, often represented by "x" or "y" but any
letter will do!
Linear a mathematical statement that performs functions of addition,
Expression: subtraction, multiplication, and division
However, variable(s) in linear expressions
•
•
•
Cannot have exponents (or powers)
For example, x squared or x 2
Cannot multiply or divide each other
For example: "x" times "y" or xy; "x" divided by "y" or x/y
Cannot be found under a root sign or square root sign (sqrt)
For example: √ x or the "square root of x"; sqrt (x)
These are examples of
linear expressions:
These are not linear expressions:
(no exponents on
x2 variables)
x+4
2x + 4
(can't multiply two
2xy + 4 variables)
2x + 4y
(can't divide two
2x / 4y variables)
(no square root sign
√ x on variables)
Linear
a mathematical expression that has an equal sign and linear expressions
Equation:
Solving example #1: find x if 2x + 4 = 10
linear
equation
steps to solve
math
First step is to isolate "x" to one side
of the equation
by subtracting 4 from both sides:
2x + 4 - 4 = 10 - 4
2x + 4 = 10
Second step is to divide both sides by
2:
2x = 6
2x / 2 = 6 / 2
x=3
Check your work with the original
equation:
Solving example #2: find x if 3x
2x + 4 = 10
(2 * 3) + 4 = 10
6 + 4 = 10
- 4 = -10
(using negatives)
linear
equation
steps to solve
math
First step is to isolate "x" to one side
of the equation
by adding 4 to both sides:
3x - 4 + 4 = -10 + 4
3x - 4 = -10
Second step is to divide both sides by
3:
3x / 3 = -6 / 3
x = -2
Check your work with the original
equation:
(3 * -2) - 4 = -10
-6 - 4 = -10
3x = -6
Solving example #3: find x if: 4x - 4y = 8
(using more than one variable)
linear
equation
steps to solve
math
4x - 4y = 8
First step is to isolate "x" to one side
of the equation
by adding 4y to both sides:
4x - 4y + 4y = 8 + 4y
4x = 8 + 4y
Second step is to divide both sides by
4:
4x / 4 = (8 + 4y) / 4
x=2+y
Check your work with the original
equation:
4 * (2 + y) - 4y = 8
8 + 4y - 4y = 8
8=8
Solving example #4: find x if: x + 32 = 12
linear equation
steps to solve
math
x + 32 = 12
(Note: since the square is First step is to square the
on the number
number:
and not on the variable,
x + 32 = 12
x + 9 = 12
the expression qualifies as
a linear expression.
Second step is to subtract
both sides by 9:
x + 9 - 9 = 12 - 9
x =3
Check your work with
the original equation:
3 + 32 = 12
3 + 9 = 12
12 = 12
Flash exercise by Jay Austin and Jordan Noll, College of Design; Brad Hokanson, faculty, College of Design,
University of Minnesota, St. Paul, MN; with refinements by: Steve Kladstrup, Independent Flash Developer,
Minneapolis, MN.
Reference: www.studygs.net