Algebra Equation

What is an Equation?

An equation says that two things are equal. It will have an equals sign "=" like this:

x

−

2

=

4

That equations says: what is on the left (x − 2) is equal to what is on the right (4)

So an equation is like a statement "this equals that"

What is a Solution?

A Solution is a value we can put in place of a variable (such as x) that makes the equation true.

Example: x − 2 = 4

When we put 6 in place of x we get:

6 − 2 = 4

which is true

So x = 6 is a solution.

How about other values for x ?

• For x=5 we get "5−2=4" which is not true, so x=5 is not a solution.
• For x=9 we get "9−2=4" which is not true, so x=9 is not a solution.
• etc

In this case x = 6 is the only solution.

More Than One Solution

There can be more than one solution.

Example: (x−3)(x−2) = 0

When x is 3 we get:

(3−3)(3−2) = 0 × 1 = 0

which is true

And when x is 2 we get:

(2−3)(2−2) = (−1) × 0 = 0

which is also true

So the solutions are:

x = 3, or x = 2

When we gather all solutions together it is called a Solution Set

The above solution set is: {2, 3}

Solutions Everywhere!

Some equations are true for all allowed values and are then called Identities

Example: sin(−θ) = −sin(θ) is one of the Trigonometric Identities

Let's try θ = 30°:

sin(−30°) = −0.5 and

−sin(30°) = −0.5

So it is true for θ = 30°

Let's try θ = 90°:

sin(−90°) = −1 and

−sin(90°) = −1

So it is also true for θ = 90°

Is it true for all values of θ? Try some values for yourself