what's an exampe of a basic algebratic equation?

Question

I'm writing notes for a kind of important maths exam tomorrow, and I wanted to have a few notes on basic algebraic equations, but I'm not actually sure what they are..?

Answer 1

Here is an example of an algebraic equation:

 

2x + 6 = 30

 

The equation tells us that some number is multiplied by 2, and the product is added to 6.  As a result, we get a value of 30.

 

When we have an equation such as this one, we want to solve for the variable.  In this case, the variable is x.

 

Here is how we solve.  We want to isolate x to one side of the equation.

 

 

First step:  Subtract 6 on both sides of equation.  We do this because we need to keep the equation balanced.

 

2x + 6 - 6 = 30 - 6

 

Positive 6 and negative 6 cancel each other out on the left side of equation.  We end up with

 

2x = 24

 

The equation is now becoming simpler to solve.

 

 

Second Step: Divide both sides of the equation by the coefficient of x.  This will allow us to get a coefficient of 1 for x, since we want x.  In this example, we divide both sides of the equation by 2.  This is because 2x divided by 2 gives us 1x, and 1 times x is x.

 

 

2x / 2 = 24 / 2

 

x = 12

 

The value of x is 12.

 

Next is to check this value of x.  We do this by plugging the value into the equation.

 

2x + 6 = 30

 

2(12) + 6 = 30

 

24 + 6 = 30

 

      30 = 30

 

Notice that the number to the left of the equal sign is the same as the number to the right of the equal sign.  This indicates that the value of x is correct.  In the event both sides did not match, we would have to go back to see where the mistake was made in the algebra.