# How to Solve Two-Step Equations

- Math Lessons >
- Two-step Equations

What is a two-step equation?

As the name suggests, a two-step equation requires two steps to solve a problem. A two-step equation has more than one operation.

An example of two-step equation is

9k + 3 = 21

How do you solve a two-step equation?

It doesn't take much to solve a two-step equation. Isolate the variable to solve the equation. To isolate the variable, use inverse operations wherever required.

Let's consider the below instance:

5x + 7 = 17

Step 1: In the above-given equation, undo the addition using inverse operations (subtraction) on both sides of the equation.

5x = 10

Step 2: To remove the coefficient of the variable, perform the inverse of multiplication (division). Divide by 5 on both sides of the equation.

x = 2

Check your solution!

Plug-in the value of the variable in the equation to check your answer.

For the equation 5x + 7 = 17, substitute x = 2,

(5 × 2) + 7 = 17

10 + 7 = 17

17 = 17 ✔

The lesson in a nutshell:

⮚ To obtain the value of a variable, we have to isolate the variable.

⮚ Perform inverse operations on both sides of the equation to isolate the variable.

⮚ Simplify the equation and find the value of the variable.

⮚ Check your answer by substituting the variable value in the equation.

Boost your skills using our free printable worksheets on Two-step Equations.

Solved Examples:

Example 1

1. Solve 4x – 7 = 15

4x – 7 = 15

4x – 7 + 7 = 15 + 7

[ Adding 7 on both sides ]

4x = 22

*4x***4** = *22***4**

[ Dividing by 4 on both sides ]

x = *11***2**

Example 2

2. Solve 8y = 40 – 2y

8y = 40 – 2y

8y + 2y = 40 – 2y + 2y

[ Adding 2y on both sides ]

10y = 40

*10y***10** = *40***10**

[ Dividing by 10 on both sides ]

y = 4

Example 3

3. On a clearance sale, a jumpsuit was up for grabs at half the price. Sara grabs the deal, and she further uses a coupon for $7. If she pays $21 to the cashier, what was the original cost of the jumpsuit?

The above scenario forms an equation: , where k refers to the original cost of the jumpsuit.

*k***2** – 7 = 21

*k***2** – 7 + 7 = 21 + 7

[ Adding 7 on both sides ]

*k***2** = 28

*k***2** × 2 = 28 × 2

[ Multiplying 2 on both sides ]

k = 56

The original cost of the jumpsuit is $56.