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Definitions:
Variable:
a number that you don't know, often represented by "x"
or "y" but any letter will do!
Linear Expression:
a mathematical statement that performs functions
of addition, 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:
Ö
x or the "square root
of x"; sqrt (x)
These are examples of linear expressions:
x + 4
2x + 4
2x + 4y
These are not linear expressions:
x2
(no exponents on variables)
2xy + 4
(can't multiply two variables)
2x / 4y
(can't divide two variables)
Ö
x
(no square root sign on
variables)
Linear Equation:
a mathematical expression that has an equal sign and
linear expressions
Solve these linear equations: (If your computer does not have
Flash, proceed to manual exercises below)
Solving example #1: find x if 2x + 4 = 10
linear equation
steps to solve
math
2x + 4 = 10
First step is to isolate "x" to one side of the equation
by subtracting 4 from both sides:
2x + 4 - 4 = 10 - 4
2x = 6
Second step is to divide both sides by 2:
2x / 2 = 6 / 2
x = 3
Check your work with the original equation:
2x + 4 = 10 (2 * 3) + 4 = 10 6 + 4 = 10
Solving example #2: find x if 3x
- 4 = -10 (using negatives)
linear equation
steps to solve
math
3x - 4 = -10
First step is to isolate "x" to one side of the equation
by adding 4 to both sides:
3x - 4 + 4 = -10 + 4
3x = -6
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
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 on the
number and not on the variable, the expression qualifies as a linear expression.
First step is to square the number:
x
+ 32 = 12 x + 9
= 12
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.
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