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The order and connection
of ideas
is the same as the order
and connection of things.
Baruch (Benedict) Spinoza
1623 - 1677 Dutch philospher

Math series

Solving Linear Equations

Linear Equation:
a mathematical expression that has an equal sign and linear expressions

Variable:
a number that you don't know, often represented by "x" or "y"
but any letter will do!

Variable(s) in linear expressions

  • Cannot have exponents (or powers)
    For example, x squared or x2
  • 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 x"; sqrt (x)

Linear Expression:
a mathematical statement that performs
functions of addition, subtraction, multiplication, and division

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)
√x (no square root sign on variables)

Solve these linear equations by clicking and dragging
a number to the "other" side of the equal sign.
Remember that you are "isolating" the unknown "X" to solve the problem.
(More examples are provided below.)


More examples:

Linear equation, solving example #1:

Find x if: 2x + 4 = 10

1.

Isolate "x" to one side of the equation
by subtracting 4 from both sides:
2x + 4 - 4 = 10 - 4

2x = 6

2. Divide both sides by 2: 2x / 2 = 6 / 2

x = 3

3. Check your work with the original equation: 2x + 4 = 10
(2 * 3) + 4 = 10
6 + 4 = 10

Linear equation, solving example #2:

Find x if: 3x - 4 = -10
(using negatives)

1.

Isolate "x" to one side of the equation
by adding 4 to both sides:
3x - 4 + 4 = -10 + 4

3x = -6

2. Divide both sides by 3: 3x / 3 = -6 / 3
x = -2
3. Check your work with the original equation: (3 * -2) - 4 = -10
-6 - 4 = -10

Linear equation, solving example #3:

Find x if: 4x - 4y = 8
(using more than one variable)

1.

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
2. Second step is to divide both sides by 4: 4x / 4 = (8 + 4y) / 4
x = 2 + y
3. Check your work with the original equation: 4 * (2 + y) - 4y = 8
8 + 4y - 4y = 8
8 = 8

Linear equation, solving example #4:

Find x if: x + 32 = 12
Note: since the square is on the number and not on the variable,
the expression qualifies as a linear expression
1. First step is to square the number: x + 32 = 12
x + 9 = 12
2. Second step is to subtract both sides by 9: x + 9 - 9 = 12 - 9
x = 3
3. Check your work with the original equation: 3 + 32 = 12
3 + 9 = 12
12 = 12

Math series

Math exams | Solving linear equations | Solving math word problems, introdution |
Word problems, exercise I | Word problems, II | Word problems, III |
Evaluating algebraic expressions | Creating and developing spreadsheets |
P.E.M.D.A.S.: 2nd exercise | P.E.M.D.A.S.: 3rd exercise | Sudoku 数独

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.