How to Solve Two-Step Equations
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- 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
4x4 = 224
[ Dividing by 4 on both sides ]
x = 112
Example 2
2. Solve 8y = 40 – 2y
8y = 40 – 2y
8y + 2y = 40 – 2y + 2y
[ Adding 2y on both sides ]
10y = 40
10y10 = 4010
[ 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.
k2 – 7 = 21
k2 – 7 + 7 = 21 + 7
[ Adding 7 on both sides ]
k2 = 28
k2 × 2 = 28 × 2
[ Multiplying 2 on both sides ]
k = 56
The original cost of the jumpsuit is $56.
