How to Solve, Check & Graph Linear Equations

Linear equations are mathematical expressions that contain at least one variable (letters such as "x" and "y" that represent unspecified numbers) and output a specific point on the graph when solved. They are easy to solve, check and graph. Once you grasp the basic concept of how to solve them, you will have no problem moving onto more challenging linear equations.

Instructions

Solving Linear Equations

1. Look at the following linear equation and solve for "x." In order to solve for "x," you must first isolate "x" to one side of the equal sign.

   0 = 2x - 10

2. Add 10 to both sides of the equation. Adding 10 to negative 10 on the right side of the equation will make it zero (cancel it out) and adding 10 to zero on the left side of the equation will give you ten.

   0 = 2x - 10
   +10 = +10
   ------------------
   10 = 2x

3. Divide both sides by two to further isolate "x." Two divided by two on the right side gives you one, and ten divided by two on the left side gives you five. One multiplied by "x" is simply "x."

   10/2 = 2x/2
   5 = 1x
   5 = x

Checking Linear Equations

1. Plug the answer you got back into the equation. In this case, replace "x" in the equation with "5."

   0 = 2(5) - 10

2. Solve the equation. First multiply two by five. The answer is 10. Then subtract 10 from 10 and you will get zero.

   0 = 2(5) - 10
   0 = 10 - 10
   0 = 0

3. Check to see that both sides of the equation are equal. If they are, you have successfully solved the equation. If they are not equal, then you have made a mistake. In this case, zero equals zero; therefore, it is true that "x" equals "5" in this equation.

Graphing Linear Equations

1. Create a number line, by drawing a line and labeling it with numbers, such as the one below.

   <==[]==[]==[]==[]==[]==[]==[]==[]==>
   0 1 2 3 4 5 6 7 8 9

2. Take the value you found for "x," in this case it was "5," and draw a solid dot on the number line where you see the number "5."

   <==[]==[]==[]==[]==[•]==[]==[]==[]==>
   0 1 2 3 4 5 6 7 8 9

3. Check to see that your number line corresponds with your linear equation. In this case, there was an equal sign in the equation; therefore, there will only be one solid dot on the number line that corresponds with the equation.

   0 = 2x - 10

   <==[]==[]==[]==[]==[•]==[]==[]==[]==>
   0 1 2 3 4 5 6 7 8 9

References

• Study Guides and Strategies: Solving Linear Equations
• Math Warehouse: How to Graph the Equation of a Linear Inequality