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Two Step Equations

Grade 7 Math Worksheets

A two-step equation is an algebraic equation that can be solved in two steps. The goal is to isolate the variable (usually represented by x) on one side of the equation.

Table of Contents:

  • What is Two Step Equation?
  • Solved Examples
  • FAQs 

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Two Step Equations - Grade 7 Math Worksheet PDF

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What is Two Step Equation?

A two-step equation is an algebraic equation that can be solved in two steps. The goal is to isolate the variable (usually represented by x) on one side of the equation.

Here are the steps to solve a two-step equation:

Step 1: Simplify the equation using the order of operations (PEMDAS) to remove any parentheses and combine like terms.

Step 2: Isolate the variable on one side of the equation by performing inverse operations. To do this, perform the opposite operation of what is being done to the variable in the equation. For example, if the variable is being added to or subtracted from, perform the opposite operation by subtracting or adding the same amount to both sides of the equation.

Here’s an example of how to solve a two-step equation:

Two Step Equation

Example: Solve the equation 4x + 3 = 19

Step 1: Simplify the equation by subtracting 3 from both sides because it is an equation and we have to balance it on both sides.:

4x + 3 – 3 = 19 – 3

4x = 16

Step 2: Isolate the variable by dividing both sides by 4:

4x/4 = 16/4

x = 4

Therefore, the solution to the equation 4x + 3 = 19 is x = 4.

Note that in this example, we used the inverse operation of addition (subtraction) and the inverse operation of multiplication (division) to isolate the variable on one side of the equation.

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Two-Step Equations Solved Examples 

Example 1: Solve the equation 2x + 4 = 10

Step 1: Simplify the equation by subtracting 4 from both sides:

2x + 4 – 4 = 10 – 4

2x = 6

Step 2: Isolate the variable by dividing both sides by 2:

2x/2 = 6/2

x = 3

Therefore, the solution to the equation 2x + 4 = 10 is x = 3.

 

Example 2: Solve the equation 5x – 7 = 18

Step 1: Simplify the equation by adding 7 to both sides:

5x – 7 + 7 = 18 + 7

5x = 25

Step 2: Isolate the variable by dividing both sides by 5:

5x/5 = 25/5

x = 5

Therefore, the solution to the equation 5x – 7 = 18 is x = 5.

 

Example 3: Solve the equation 3(x + 2) = 21

Step 1: Simplify the equation by using the distributive property and combining like terms.To use the distributive property, we will multiply 3 with individual terms inside the parenthesis. So 3 multiply by x and again 3 will multiply by +2. It will give a clear idea of the solution.

3x + 6 = 21

Step 2: Isolate the variable by subtracting 6 from both sides:

3x + 6 – 6 = 21 – 6

3x = 15

Step 3: Isolate the variable by dividing both sides by 3:

3x/3 = 15/3

x = 5

Therefore, the solution to the equation 3(x + 2) = 21 is x = 5.

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Two-Step Equations FAQS

What are two-step equations?

Two-step equations are algebraic equations that can be solved in two steps by isolating the variable on one side of the equation.

What is the order of operations in two-step equations?

The order of operations in two-step equations is to first simplify the equation by using parentheses and combining like terms. Then, isolate the variable on one side of the equation by performing the inverse operation of what is being done to the variable.

What is the inverse operation?

The inverse operation is the opposite of a given mathematical operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Can two-step equations have variables on both sides of the equation?

No, two-step equations only have variables on one side of the equation. If there are variables on both sides of the equation, it is a different type of equation that requires a different method to solve.

What happens if I make a mistake while solving a two-step equation?

If you make a mistake while solving a two-step equation, it can affect the final solution. It’s important to check your work and make sure that your solution makes sense in the context of the original equation.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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