Two-Step Equation Calculator
Solve equations in the form ax + b = c with step-by-step solutions
Examples: 2x + 5 = 13, 3x - 7 = 14, -4x + 10 = 2
How to Solve Two-Step Equations
A two-step equation is a linear equation that requires exactly two inverse operations to solve. The standard form is ax + b = c, where you need to undo addition/subtraction first, then multiplication/division.
The Two-Step Process
Step 1: Eliminate the constant term
Use addition or subtraction to move the constant (b) to the other side of the equation.
Step 2: Eliminate the coefficient
Use multiplication or division to isolate the variable by removing the coefficient (a).
Example Problem
Solve: 3x + 7 = 22
Step 1: Subtract 7 from both sides
3x + 7 - 7 = 22 - 7
3x = 15
Step 2: Divide both sides by 3
3x ÷ 3 = 15 ÷ 3
x = 5
Check: 3(5) + 7 = 15 + 7 = 22 ✓
Key Points to Remember
- Always perform operations in reverse order of PEMDAS
- Undo addition/subtraction before multiplication/division
- Whatever you do to one side, do to the other
- Check your answer by substituting back into the original equation
Frequently Asked Questions
What is a two-step equation?
A two-step equation is a linear equation that requires exactly two inverse operations to solve. It typically has the form ax + b = c, where both multiplication and addition (or subtraction) are involved.
Why do we solve in two steps?
We follow the reverse order of operations (PEMDAS). Since multiplication comes before addition in order of operations, we undo addition first, then undo multiplication. This ensures we correctly isolate the variable.
Can I solve the steps in any order?
For standard two-step equations (ax + b = c), you should eliminate the constant term first, then the coefficient. Doing them in reverse order leads to fractions and makes the problem more complicated.
What if my equation has subtraction instead of addition?
Equations like 2x - 5 = 11 work the same way. In step 1, you add 5 to both sides (the inverse of subtracting 5). Then proceed with step 2 as normal.
How do I handle negative coefficients?
With negative coefficients like -3x + 7 = 1, follow the same process. Subtract 7 to get -3x = -6, then divide by -3 to get x = 2. Remember that dividing two negatives gives a positive.
What if my answer is a fraction?
It's perfectly normal for solutions to be fractions or decimals. For example, 2x + 3 = 8 gives x = 5/2 or x = 2.5. Both forms are correct.
How is this different from a one-step equation?
One-step equations like x + 5 = 12 or 2x = 10 require only one operation to solve. Two-step equations like 2x + 5 = 15 require two operations: first subtract 5, then divide by 2.
Why is it important to check my answer?
Checking your answer by substituting it back into the original equation verifies that you solved correctly. It helps catch arithmetic errors and confirms that your solution satisfies the equation.