A one-step equation is an algebraic equation that can be solved by performing only one mathematical operation. It involves a single variable, and its value is found by applying one inverse operation to both sides of the equation.
Examples of one-step equations are
- x + 5 = 12 ⟹ x = 7
- 4z = 20 ⟹ z = 5
One-step equations can be used in real life in many ways:
1) A car travels 120 miles at a constant speed of 60 miles per hour. Here, if we want to find the time taken for the journey, we can use the following one-step equation:
- Let t represent time. The equation is 60t = 120.
2) 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.
General Form
A one-step equation can be represented in different forms depending on the mathematical operation involved.
- Addition: x + a = b
- Subtraction: x - a = b
- Multiplication: ax = b
- Division: x / a = b
Steps to Solve
A one-step equation is solved by isolating the variable using the appropriate inverse operation. Follow the steps below:
Step 1: Identify the mathematical operation applied to the variable.
Step 2: Determine the inverse (opposite) of that operation.
(Addition ↔ Subtraction, Multiplication ↔ Division)
Step 3: Apply the inverse operation to both sides of the equation to maintain equality.
- If the variable is multiplied by a number, divide both sides by that number.
- If the variable is divided by a number, multiply both sides by that number.
- If a number is added to the variable, subtract the same number from both sides.
- If a number is subtracted from the variable, add the same number to both sides.
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.
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
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
Properties
1. Addition Property of Equality: If a = b, then a + c =b + c
2. Subtraction Property of Equality : If a = b, then a − c = b − c
3. Multiplication Property of Equality : If a = b, then ac = bc
4. Division Property of Equality : If a = b, then ca = cb, c ≠ 0