Mastering Two-Step Algebraic Equations

1. Understand the Problem

The first step to solving a two-step algebraic equation is to clearly write down the problem. This helps you visualize the solution process. For our example, we will work with the equation: -4x + 7 = 15.

2. Isolate the Variable Term Using Addition or Subtraction

The next step is to isolate the variable term (e.g., "-4x") on one side of the equation and the constants (whole numbers) on the other. To achieve this, you'll use the Additive Inverse. Find the opposite of the constant term on the same side as the variable. In our example, the constant is +7, so its additive inverse is -7.

Subtract 7 from both sides of the equation to cancel out the "+7" on the variable's side. Write "-7" below the 7 on the left side and below the 15 on the right side to maintain the equation's balance.

Important Algebra Rule: The Golden Rule

Remember the Golden Rule of Algebra: Whatever you do to one side of an equation must be done to the other side to maintain balance. This is why 7 is subtracted from 15 as well. We only need to subtract 7 once per side; therefore, 7 is not subtracted from the -4x term.

3. Complete the Constant Isolation

This step completes the process of isolating the variable term. Subtracting 7 from +7 on the left side of the equation will result in zero (no constant term) on that side. Subtracting 7 from +15 on the right side of the equation will leave you with 8. Therefore, the new simplified equation is:

• Original: -4x + 7 = 15
• After subtraction: -4x = 8

4. Eliminate the Variable's Coefficient

The coefficient is the number directly attached to the variable. In our example, the coefficient is -4. To remove the -4 from -4x, you must perform the inverse operation. Since x is currently being multiplied by -4, the opposite operation is division. You will need to divide both sides of the equation by -4.

Maintaining Balance

Again, remember that any operation performed on one side of the equation must be applied to the other side. This is why you will divide both sides by -4.

5. Solve for the Variable

To find the value of the variable, divide the left side of the equation, -4x, by -4, which gives you x. Then, divide the right side of the equation, 8, by -4, which results in -2. Therefore, the solution is: x = -2.

You have successfully solved this two-step equation by applying two key operations: subtraction and division.