Solving Two-Step Equations

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.

1. Add or subtract to isolate the variable term.
2. Multiply or divide to solve for the variable.
3. Check your solutions.

Algebra Worksheets
Practice your skills with the following Algebra worksheets:
Printable & Online Algebra Worksheets

Key Principles to Remember:

1. 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).
2. Inverse Operations: Use the opposite operation to undo what’s being done to the variable (addition/subtraction, multiplication/division).
3. Keep the Equation Balanced: Perform the same operation on both sides of the equation to maintain equality.
4. 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

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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:

1. 2x + 1/4 = 3/5
2. 2/5 x - 1/2 = 3/5
3. 1/4 = 3/5 x - 5
4. 2 1/5 = 2/3 - 1/2 x

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How To Solve Two Step Linear Equations Involving Decimals?

Examples:

1. 0.3x - 2.16 = 9.9
2. x/2.1 + 4.93 = 10.45

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How To Solve The Different Types Of Two Step Equations?

Examples:

1. 2x + 3 = 25
2. x/4 - 2 = -5
3. 4 - 2x = 10
4. 4 = 6 - x/3
5. 4.3 = 1.5x - 5
6. x/3 - 3/4 = 1/6

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Examples Of Solving Two-Step Equations

1. b/3 + 13 = 11
2. 9g + 11 = 2
3. t/4 - 10 = -6
4. -a + 6 = 8
5. 15x + 3 = 48

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How To Solve A Two-Step Equation? (undo PEMDAS in reverse to solve)

Example:
4x + 8 = 24

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Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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