The order and connection of ideas
is the same as the order
and connection of things.
Baruch (Benedict) Spinoza
1623-1677, Dutch
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!
Linear
Expression:
a mathematical statement that performs functions of addition, subtraction, multiplication, and division
Note: 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)
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.
(Examples are provided below.)
Solving example #1: find x if 2x + 4 = 10
linear equation #1:
steps to solve
2x + 4 = 10
math
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
Solving example #2: find x if 3x - 4 = -10
(using negatives)
linear equation #2:
steps to solve
3x - 4 = -10
math
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
Solving example #3: find x if: 4x - 4y = 8
(using more than one variable)
linear equation #3:
steps to solve 4x - 4y = 8
math
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
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
linear equation #4
steps to solve x + 32 = 12
math:
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
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