Overview
This lecture explains how to solve two-step algebraic equations by isolating the variable, using inverse operations, and checking the solution.
What is a Two-Step Equation?
- A two-step equation is an algebra equation that requires two operations to isolate the variable.
Steps to Solve a Two-Step Equation
- Identify the variable (e.g., X) to isolate in the equation.
- Use the inverse operation to move the constant term from the variable side to the other side (e.g., subtract 3 from both sides).
- Simplify both sides after each operation.
- If the variable is multiplied by a coefficient, divide both sides by that number to isolate the variable.
- The goal is to get the variable alone on one side of the equation.
Example: Solving 7x + 3 = 38
- Subtract 3 from both sides: 7x + 3 - 3 = 38 - 3 → 7x = 35.
- Divide both sides by 7: 7x/7 = 35/7 → x = 5.
Checking the Solution
- Substitute x = 5 back into the original equation: 7(5) + 3 = 38.
- Compute: 35 + 3 = 38, which confirms the solution is correct.
Key Terms & Definitions
- Two-Step Equation — An equation that needs two operations to solve for the variable.
- Inverse Operation — The mathematical operation that reverses the effect of another (e.g., subtraction is the inverse of addition).
Action Items / Next Steps
- Practice solving additional two-step equations.
- Always check your solution by substituting it back into the original equation.