One Step Equations

A one-step equation is a type of algebraic equation that requires only one operation (like addition, subtraction, multiplication, or division) to solve for the unknown variable.
Example:

• x + 5 = 12 ⟹ x = 7
• y − 3 = 10 ⟹ y = 13
• 4z = 20 ⟹ z = 5

To solve these equations you need to move the variable on one side of the equal sign and the constants on the other side. These equations are known to be straightforward forms of an algebraic expression and are most frequently used to explain the basic principles of solving algebraic equations to learners.

One-step equations can be used in real life in many ways:

• A car travels 120 miles at a constant speed of 60 miles per hour. Here, if we want to find the time taken for journey, we can use the following one step equation:
  • Let t represent time. The equation is: 60t = 120.
• A recipe calls for 4 cups of flour, but you want to make half the recipe. How many cups of flour should you use?
  • Let x represent the new amount of flour. The equation is: x/2 = 4.
• You buy a shirt with a 20% discount, and you know the final price is £32. What was the original price?
  • Let the original price be x. The equation becomes: x − 0.2x = 32 or 0.8x = 32

How to Solve One -Step Equations

Solving one -step equations involves identifying the operation applied to the variable and performing the inverse operation to isolate it. For each operation there is an inverse operation which reverses it's application i.e.,

Below are methods based on different operations.

Solving One -Step Equations Using Addition and Subtraction

In equations involving addition or subtraction, we isolate the variable by performing the opposite operation on both sides of the equation. Here's how:

Example: Solve x -7 = 10.

Solution:

Since 7 is subtracted, add 7 to both sides:
x -7 + 7 = 10 + 7
⇒x = 17

Example: Solve y + 5 = 9.

Solution:

Since 5 is added, subtract 5 from both sides:
y + 5 -5 = 9 -5
⇒ y = 4

In both examples, we apply the inverse of the given operation to isolate the variable.

Solving One -Step Equations Using Multiplication and Division

For equations involving multiplication or division, we isolate the variable by performing the opposite operation on both sides.

Example: Solve 4x = 16

Solution:

Since 4 is multiplied, divide both sides by 4:
4x/4 = 16/4
⇒x = 4

Example: Solve y/6 = 3.

Solution:

Multiply both sides by 6 to cancel the division:
y/6 × 6 = 3 × 6
⇒ y = 18

These operations illustrate the core concept of balancing an equation by performing the inverse operation on both sides.

Solved Examples on One-Step Equations

Example 1: Solve the equation: x − 4 = 9

Solution:

The equation involves subtraction, so we add 4 to both sides to isolate
x − 4 + 4 = 9 + 4
Simplifying both sides: x = 13

Answer: x = 13.

Example 2: Solve the equation: y + 7 = 15

Solution:

The equation involves addition, so subtract 7 from both sides to isolate y.
y + 7 − 7 = 15 − 7
Simplifying both sides: y = 8

Answer: y = 8.

Example 3: Solve the equation: 5z = 20

Solution:

The equation involves multiplication, so divide both sides by 5 to isolate
5z/5 = 20/5
Simplifying both sides: z = 4

Answer: z = 4.

Example 4: Solve the equation: x/6 = 2

Solution:

The equation involves division, so multiply both sides by 6 to isolate
x/6 × 6 = 2 × 6
Simplifying both sides: x = 12

Answer: x = 12.

Example 5: Solve the equation: − 3b = 12

Solution:

The equation involves multiplication by a negative number, so divide both sides by − 3 to isolate b.
− 3b/ -3 = 12/ -3
Simplifying both sides: b = − 4

Answer: b = − 4.

Also Read: One Step Equations Practice Questions

Worksheet On One Step Equations

You can download free worksheet on one step equations from below:

Conclusion

One-step equations provide the foundation for solving algebraic problems efficiently. They are used as building blocks towards appreciating other more difficult concepts in mathematics. Besides, problems that involve isolating variables by using inverse operations not only help students improve their mathematical problem -solving ability, but also apply to many life care situations including money management, geometry, and science.

Read More,

• Equations in Maths
• Expressions
• Variable in Maths