Two-Step Equations

Solving two-step equations involves isolating the variable by performing inverse operations. These equations typically require two operations to solve.

Rules for Solving Two-Step Equations

1. Identify the Variable: Locate the unknown variable (e.g., $x$, $y$) in the equation.

2. Undo Addition or Subtraction: First, eliminate any constant term that is being added to or subtracted from the variable term. Perform the inverse operation on both sides of the equation.

   • If a number is added, subtract it from both sides.

   • If a number is subtracted, add it to both sides.

   • Example: In $2x + 5 = 11$, subtract $5$ from both sides: $2x = 6$.

3. Undo Multiplication or Division: Next, eliminate the coefficient (the number multiplying the variable). Perform the inverse operation on both sides of the equation.

   • If the variable is multiplied by a number, divide both sides by that number.

   • If the variable is divided by a number, multiply both sides by that number.

   • Example: In $2x = 6$, divide both sides by $2$: $x = 3$.

4. Check Your Solution (Optional but Recommended): Substitute your solution back into the original equation to ensure both sides are equal.

   • Example: For $x=3$ in $2x + 5 = 11$, we have $2(3) + 5 = 6 + 5 = 11$. Since $11 = 11$, the solution is correct.

General Form

A two-step equation often takes the form $ax + b = c$, where:

• $a$ is the coefficient of the variable $x$

• $b$ is a constant term being added or subtracted

• $c$ is the constant on the other side of the equation.