An equation is a mathematical statement that two things are equal to each other or that two things are conditionally equal to each other.^{[2]} If an equation is true for all values of any variables in the equation, it is called an identity. Identities are sometimes written using the symbol ≡ to indicate that they are always true.
Identity | Description |
---|---|
a + 0 ≡ a | The additive identity |
a · 1 ≡ a | The multiplicative identity |
sin(θ)^{2} + cos(θ)^{2} ≡ 1 | The Pythagorean identity is one of the trigonometric identities. |
Table 1: Examples of identities |
If an equation is not true for all values of the variables, it is called a conditional equation. The values of the variables for which the equation is true is called the solution of the equation.
Equation | Description | Solution |
---|---|---|
x = 5 | This is a simple equation. | This is equation is true only when x = 5. |
y = x + 1 | This is a linear equation. | This equation is true for a set of ordered values (x,y) such that y = x + 1. |
a^{2} + 4a + 4 = 0 | This is a quadratic equation. | This equation is true only when a = -2 |
An equation can be solved using the various property of real numbers and the properties of equality When solving a one variable equation, the goal is to get the variable by itself on one side of the equation.
Equation | Discussion |
---|---|
x + 5 = 2 | This is the equation to solve. |
(x + 5)- 5 = 2 - 5 | Apply the Subtraction property of equality |
(x + 5) + (^{-}5)) = 2 - 5 | Apply the Definition of subtraction |
x + (5 + (^{-}5)) = 2 - 5 | Apply the Distributive property of multiplication over addition and subtraction. |
x + 0 = ^{-}3 | Simplify both sides of the equation. |
x = ^{-}3 | Apply the property of addition by zero |
Table 1: Solving an equation. |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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