Two step algebraic equations are relatively quick and easy -- after all, they should only take two steps. To solve a two step algebraic equation, all you have to do is isolate the variable by using either addition, subtraction, multiplication, or division. If you want to know how to solve two step algebraic equations in a variety of ways, just follow these steps.
1. Write the problem. The first step to solving a two step algebraic equation is just to write the problem so you can start to visualize the solution. Let's say we're working with the following problem: -4x + 7 = 15.
2. Decide whether to use addition or subtraction to isolate the variable term. The next step is to find a way to keep "-4x" on one side and to keep the constants (whole numbers) on the other side. To do this, you'll have to do the "Additive Inverse," finding the opposite of +7, which is -7. Subtract 7 from both sides of the equation so that the "+7" on the same side as the variable term is canceled out. Just write "-7" below the 7 on one side and below the 15 on the other so the equation remains balanced. Remember the Golden Rule of Algebra. Whatever you do to one side of an equation must be done to the other side to maintain the balance. That is why 7 is subtracted from the 15 as well. We only need to subtract 7 once per side, which is why the 7 is not subtracted from the -4x as well.
3. Add or subtract the constant on both sides of the equation. This will complete the process of isolating the variable term. Subtracting 7 from +7 on the left side of the equation will leave no constant term (or 0) on the left side of the equation. Subtracting 7 from +15, on the right side of the equation, will leave you with 8. Therefore, the new equation is -4x = 8. -4x + 7 = 15 =-4x = 84. Eliminate the coefficient of the variable through division or multiplication. The coefficient is the number attached to the variable. In this example, the coefficient is -4. To remove the -4 in -4x, you'll have to divide both sides of the equation by -4. Right now, the x is being multiplied by the -4, so the opposite of this operation is division and you'll have to do it on both sides. Again, whatever you do to the equation must be done to both sides. That is why you see ÷ -4 twice.5.Solve for the variable. To do this, divide the left side of the equation, -4x, by -4, to get x. Divide the right side of the equation, 8, by -4, to get -2. Therefore, x = -2. You've taken two steps -- subtraction and division -- to solve this equation.
