Solving Two-Step Equations
Related Pages
Solving Equations
Algebraic Expressions
More Algebra Lessons
In these lessons, we will look at solving equations that require two steps.
How to solve two-step equations?
Solving two-step equations builds upon the principles of solving one-step equations. The goal is still to isolate the variable, but it will require performing two inverse operations in the correct order.
The following figure shows how to solve two-step equations. Scroll down the page for more examples and solutions.
In order to solve two-step equations, we need to work backwards with regards to the order of operations. We would perform the addition & subtraction before multiplication & division.
- Add or subtract to isolate the variable term.
- Multiply or divide to solve for the variable.
- Check your solutions.
Algebra Worksheets
Practice your skills with the following Algebra worksheets:
Printable & Online Algebra Worksheets
Key Principles to Remember:
- Work Backwards: When solving for a variable, you are essentially reversing the order of operations that would be used to evaluate the expression (reverse PEMDAS).
- Inverse Operations: Use the opposite operation to undo what’s being done to the variable (addition/subtraction, multiplication/division).
- Keep the Equation Balanced: Perform the same operation on both sides of the equation to maintain equality.
- Check Your Answers: Substitute your solution back into the original equation to verify its correctness.
Example:
Solve 3x – 2 = 16
Solution:
In the equation 3x – 2 = 16, notice that the variable is being multiplied and has a term
being subtracted. To isolate the variable, we need to add 2 to both sides and then divide both
sides by 3.
3x – 2 = 16
3x – 2 + 2 = 16 + 2 (add 2 to both sides)
3x = 18 (simplify)
x = 6 (divide both sides by 3)
Check:
3x – 2 = 16
3 • 6 – 2 = 16 (Substitute x = 6 into the original equation)
Example:
Solve 
Solution:
Consider the equation, . To isolate the variable, we need to subtract 2 from both sides and then multiply
both sides by 4.
Check:
How To Solve Basic Two Step Equations?
Examples:
a) 2x + 3 = 9
b) 5x – 8 = 22
c) 9 – 2x = 23
d) –11 = 4x – 43
e) –15 = 5 – 5x
How To Solve Two Step Linear Equations With Fractions?
In this video, the equations are solve by working with the fraction, not be clearing the fractions from the equation.
Examples:
- 2x + 1/4 = 3/5
- 2/5 x - 1/2 = 3/5
- 1/4 = 3/5 x - 5
- 2 1/5 = 2/3 - 1/2 x
How To Solve Two Step Linear Equations Involving Decimals?
Examples:
- 0.3x - 2.16 = 9.9
- x/2.1 + 4.93 = 10.45
How To Solve The Different Types Of Two Step Equations?
Examples:
- 2x + 3 = 25
- x/4 - 2 = -5
- 4 - 2x = 10
- 4 = 6 - x/3
- 4.3 = 1.5x - 5
- x/3 - 3/4 = 1/6
Examples Of Solving Two-Step Equations
- b/3 + 13 = 11
- 9g + 11 = 2
- t/4 - 10 = -6
- -a + 6 = 8
- 15x + 3 = 48
How To Solve A Two-Step Equation? (undo PEMDAS in reverse to solve)
Example:
4x + 8 = 24
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