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	<="" td=""> (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 - 42x = 6
2.	Divide both sides by 2:	2x / 2 = 6 / 2x = 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 + 43x = -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