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Two-Step Equations

What are Two-Step Equations?

Two-step equations are algebraic equations that require two operations to solve for the variable. They typically involve both addition/subtraction and multiplication/division.

Standard Form of a Two-Step Equation

ax + b = c

Where a, b, and c are constants, and x is the variable we're solving for.

To solve, we need to isolate the variable by performing two operations:

  1. Subtract or add to get the variable term alone on one side.
  2. Multiply or divide to isolate the variable.

Interactive Two-Step Equation Solver

Use this interactive tool to solve two-step equations of the form ax + b = c. Adjust the values to see the solution steps.

Enter Your Equation: ax + b = c

Your Equation:

2x + 3 = 7

Solution Steps:

2x + 3 = 7
2x + 3 - 3 = 7 - 3
2x = 4
2x / 2 = 4 / 2
x = 2

Solving Two-Step Equations

Example 1: 3x + 4 = 13

Let's solve this step by step:

3x + 4 = 13
Step 1: Subtract 4 from both sides to isolate the term with the variable.
3x + 4 - 4 = 13 - 4
3x = 9
Step 2: Divide both sides by 3 to isolate the variable.
3x ÷ 3 = 9 ÷ 3
x = 3

Example 2: 2x - 7 = 5

Let's solve this step by step:

2x - 7 = 5
Step 1: Add 7 to both sides to isolate the term with the variable.
2x - 7 + 7 = 5 + 7
2x = 12
Step 2: Divide both sides by 2 to isolate the variable.
2x ÷ 2 = 12 ÷ 2
x = 6

Example 3: -4x + 10 = -6

Let's solve this step by step:

-4x + 10 = -6
Step 1: Subtract 10 from both sides to isolate the term with the variable.
-4x + 10 - 10 = -6 - 10
-4x = -16
Step 2: Divide both sides by -4 to isolate the variable.
-4x ÷ (-4) = -16 ÷ (-4)
x = 4

Word Problems with Two-Step Equations

Two-step equations are often used to solve real-world problems. Here are some examples:

Example 1: Concert Tickets

A concert venue charges $15 per ticket plus a one-time service fee of $5. If the total cost for a group was $80, how many tickets were purchased?

Step 1: Define the variable.
Let x = the number of tickets purchased.
Step 2: Write the equation.
15x + 5 = 80
Step 3: Solve the equation.
15x + 5 - 5 = 80 - 5
15x = 75
15x ÷ 15 = 75 ÷ 15
x = 5
Step 4: Interpret the solution.
The group purchased 5 tickets.

Example 2: Temperature Conversion

The formula to convert Celsius to Fahrenheit is F = 1.8C + 32. If the temperature is 77°F, what is the temperature in Celsius?

Step 1: Define the variable.
Let C = the temperature in Celsius.
Step 2: Write the equation.
1.8C + 32 = 77
Step 3: Solve the equation.
1.8C + 32 - 32 = 77 - 32
1.8C = 45
1.8C ÷ 1.8 = 45 ÷ 1.8
C = 25
Step 4: Interpret the solution.
The temperature is 25°C.

Related Topics

Practice Two-Step Equations

Test your knowledge with our interactive equation practice exercises.

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Equation Solver

Use our calculator to solve equations step by step.

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Tips for Solving Two-Step Equations

  • 1
    Always isolate the variable term before dividing or multiplying.
  • 2
    Remember to perform the same operation on both sides of the equation.
  • 3
    Check your answer by substituting it back into the original equation.
  • 4
    When working with fractions, consider multiplying both sides by the least common multiple (LCM) to eliminate fractions.
  • 5
    Draw a picture or diagram to help visualize word problems before setting up the equation.