Start with an expression for the left-hand side and calculate its value when x equals any fraction.
Example Solution: 2x+9=x+9 12
Practice makes perfect
We are going to write an equation which has a fraction as a solution and contains the variable x on both sides. We can start off with any linear expression for the left-hand side.
2x+9
Now let's choose that our solution will be x= 12. By substituting 12 for x into the equation, we can determine what the expression equals.
This means that the expression 2x+9 needs to be equal to 10.
2x+9=10
Let's find another expression that equals 10 when x= 12. The simplest way to do this is by writing an expression where a number n added to x equals 10.
x+n=10
To find n, we should substitute x= 12 for x.
We found another expression that equals 10 when x= 12.
x+9 12
Since both expressions equal 10 when x= 12, we can set them equal to one another. This will be our equation.
2x+9= x+9 12
Let's check our solution just to make sure. To do this we will solve our equation using the Subtraction Property of Equality.
