How do I Define Two Step Equations for Algebra 2?

By Alice Drinkworth
Algebra problems take more steps as you progress into Algebra 2.

Algebra 2 problems expand on the simpler equations learned in Algebra 1. Algebra 2 problems take two steps to solve rather than one. The variable is also not as easily defined. The basic algebraic skills are the same, however, and not difficult to master.

One-step Equations

A one-step algebraic equation can be solved in one step. The variable is represented by a letter, usually an x, n or t. The value of the variable is found by adding, subtracting, multiplying or dividing both sides of the equation to simplify the equation and isolate the variable. The goal is to have the variable on one side of the equation and numbers on the other. An example of a one-step equation is 3x = 12. To solve this equation, divide both sides of the equation by 3. The equation then reads x = 4. This means 4 is the value of your variable (x).

Two-step Equations

Two-step algebraic equations require two steps to be solved. As in one-step equations, the goal is to simplify the equation and isolate the variable on one side of the equation and numbers on the other side. Two-step equations, however, require more than one mathematical step to solve. An example of a two-step equation is 3x + 4 = 16. To solve this equation, first subtract 4 from both sides of the equation: 3x + 4 - 4 = 16 - 4. This gives you the one-step equation 3x = 12. Now solve this one-step equation as usual by dividing both sides of the equation by 3, giving you the solution of x = 4.

Define One Variable

In algebra, the object is to define, or find the value of, the variable. As problems become more complex in Algebra 2, there may be more than one variable. You can choose to solve for one or the other variable by isolating one of the variables on one side of the equation and putting the other variable and numbers on the other side. An example of a problem like this would be 3x + 4 = 6y + 10. To find the value of x, subtract 4 from both sides of the equation: 3x + 4 - 4 = 6y +10 - 4, which gives 3x = 6y + 6. Now further simplify by dividing each side of the equation by 3, which will give you the value of x: x = 2y + 2.

Define a Second Variable

The problem 3x + 4 = 6y + 10 can also be defined by finding the value of y. First, subtract 10 from both sides of the equation: 3x + 4 - 10 = 6y + 10 - 10, or 3x - 6 = 6y. Now divide both sides by 6 for your second step, which gives you 1/2 x - 1 = y. The value of y is 1/2 x - 1.

About the Author

Alice Drinkworth has been a writer and journalist since 1995. She has written for community newspapers, college magazines and Salon.com. Drinkworth earned a Bachelor of Arts in journalism from the University of Wisconsin and won a media award for her in-depth coverage of local politics. She is also a certified master gardener.