Difference between an equation and an expression

by Visitor
(United Kingdom)

Question

Solve the equation 2(3x-1)-x+7

Answer

First, I need to clarify a common misunderstanding between 'solving equation' and 'simplifying expression' before explaining the answer.

Solving Equation
Solving an equation involves finding a unknown value. Such as, finding the value of 'x' in a given equation.

Let's look at some rough examples on equations:

1. something = something
2. 1 + p - 10 = some expression
3. some expression = some other expression
4. 3x - 10 = 3

Notice something in the example above? All of the examples above have an equal sign (=). So, we can say that an equation must have an equal sign in it. Now, as for the question:

      2(3x-1)-x+7

Looks like the equal sign (=) is missing. So, the above is not an equation and there is no way we can solve for x.

Simplifying Expression
As you can guess, an expression does not have an equal sign in it. Some rough examples are:

1. something something
2. 1 + p - 10
3. 3x - 10 - x(1+y)

So now, the best we can do with an expression is to simplify it. Let's take a look at the question again:

     2(3x-1)-x+7

Yes!...this is an 'expression' because no equal sign in it and it is possible to simplify it.

Let's start...

Now, notice the brackets in 2(3x -1)? We need to remove these brackets first before we can simplify:

     2(3x -1)
     = 2(3x) -2
     = 6x -2

Now, with 2(3x-1)= 6x- 2, the expression becomes:

     2(3x-1) -x +7
     = 6x - 2 -x +7
     = 6x -x -2 +7
     = 5x + 5

We can no longer able to simplify 5x + 5. The answer is 5x + 5.

Math lessons that are helpful to understand this better:

1. Removing brackets


2. Adding like terms


3. Solving Linear Equations 1


4. Solving Linear Equations 2