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.
Steps to Solve One-Step Equations
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
Solved Problems
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
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
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
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
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