Linear equations are equations with variables to 1^{th} power. In other words, linear equations are equations with degree 1. Linear equations are mathematical statement that performs functions of addition, subtraction, multiplication, and division.
Examples:
x + 5 = 10
3x + 2 = 3x  9
6a  5 = 4
3a + 2b = 6
3n = 15
n/2 = 12
However, variable(s) in linear expressions
cannot have exponents example: x^{2}
cannot multiply or divide each other example: xy or x/y
cannot be found under a root sign or square root. example: sqrt(x)
The following are NOT linear equations:
x^{2}+2x+5=0
3a^{3}3a^{2}+2a5=0
4xy + 2 = 12
Solving Linear Equations
One Variable  One Variable  Multiple terms 
Method: Bring the variable term to one side and numbers on the other side of the equation.
Question: Solve w + 8 = 17 . The linear equation is read as: a number plus 8 equals 17.
When you see a plus sign use the subtration operation. So, subtracting 8 both sides we get
w + 8  8 = 17  8
w = 9
Question: Solve m  11 = 8. This linear equation is read as: a number minus 11 equals 8.
When you see a minus sign use the addition operation, therefore adding 11 both sides of the equation we get
m  11 + 11 = 8 + 11
m = 19
Question: Solve 4z = 36. Four times z equals 36.
4 x z = 36
dividing both sides by 4
4z / 4 = 36/4
z = 9
Question: Solve 2x = 10. Twice a number equals 10.
2x = 10
Dividing both sides by 2
2x/2 = 10/2
x = 5
Question: Solve (1/3)x = 12
x has a fractional coefficient, multiply each side by 3.
3(1/3)x = 12 x 3
x = 36
Question: Solve (2/5)x = 24
multiply each side by reciprocal of 2/5 that is 5/2
5/2 x (2/5)x = 5/2 x 24
x = 60
Question: Solve x/3 = 5.
Since x is divided by 3, multiply both sides of the equation by 3,
3(x/3) = 3 x 5
x = 15
Question: 9/3y = 3.
 Method 1:
3y/9 = 1/3
Multiply both sides by 9
9(3y/9) = 9(1/3)
3y = 9/3
3y = 3
y = 3/3 = 1
 Method 2:
9/3y =3
3y is in the denominator, so multiply both sides by 3y,
(9/3y) 3y = 3 . 3y
9 = 9y
9/9 = y
y = 1
Question: Solve 1/n = 4
 Method 1:
1/n = 4
multiply both sides by n
n(1/n) = 4 x n
1 = 4n
4n = 1
dividing both sides by 4
4n/4 = 1/4
n = 1/4
 Method 2:
1/n = 4
Inverse both sides
n = 1/4

Method: Bring the variables to one side and numbers on the other side of the equation.
Question:Solve 3x  7 = 23
add 7 both sides
3x  7 + 7 = 23 + 7
3x = 30
div each side by 3
3x/3 = 30/3
x = 10
Question:Solve 4x + 9 = 53
subtract 9 both sides
4x + 9  9 = 53  9
4x = 44
divide both sides by 4
4x/4 = 44/4
x = 11
Question:Solve (1/3)x + 2 = 7
subtracting 2 both sides
(1/3)x + 2  2 = 7  2
(1/3)x = 15
multiplying both sides by 3
3(1/3)x = 15 x 3
x = 45
Question:Solve (1/5)x  6 = 9
adding 6 both sides
(1/5)x  6 + 6 = 9 + 6
(1/5)x = 15
multiply each sides by 5
5(1/5)x = 15 x 5
x = 75
Question:Solve (2/5)x + 3 = 21
Subtracting 3 both sides
(2/5)x +3  3 = 21  3
(2/5) x = 18
Multiplying both sides be the reciprocal of 2/5 that is 5/2
5/2(2/5) x = (5/2)18
x =45
Question:10x  5 = 2x + 21, then x = ?
Bring the variables on one side and numbers on the other
Adding 5 both sides
10x  5 + 5 = 2x + 21  5
10x = 2x + 16
Subtracting 2x both sides
10x  2x = 2x + 16  2x
8x = 16
Dividing both sides be 8
8x/8 = 16/8
x = 2
Question:Solve 1/x + 5 + 3 = 10 + 1
subtracting 5 both sides
1/x + 5  5 + 3 = 10 + 1  5
1/x + 3 = 6
subtracting 3 both sides
1/x + 3  3 = 6  3
1/x = 3
x = 1/3
Question:Solve 10(x4)=5(x1)+5, then x = ?
Using distributive law
10x  40 = 5x  5 + 5
10x  40 = 5x
Adding 40 both sides
10x  40 + 40 = 5x + 40
10x = 5x + 40
Subtracting 5x both sides
10x  5x = 5x + 40  5x
5x =40
Dividing both sides by 5
5x/5 =40/5
x = 8

Directions: Solve the following linear equations. Also write at least 10 examples of your own.
