In the realm of algebra, the equation “the difference of twice a number and 3 is 21” presents an intriguing challenge that invites us to unravel its secrets. This equation, when solved, unveils the hidden value of the unknown number, providing a valuable lesson in algebraic problem-solving.
Our journey begins with understanding the concept of variables, which act as placeholders for unknown quantities. We assign a variable, let’s call it “x,” to represent the unknown number in our equation.
The Difference of Twice a Number and 3 is 21
In mathematics, we often encounter expressions involving unknown numbers. To solve such expressions, we use algebraic variables to represent the unknown and form equations based on the given information. This article will guide you through the steps involved in solving the expression “the difference of twice a number and 3 is 21.”
Variable Representation, The difference of twice a number and 3 is 21
To begin, we assign a variable to represent the unknown number. Let’s use the variable “x” to represent the number. This means that “twice a number” can be expressed as “2x.”
Equation Formation
Next, we create an equation based on the given information. The expression states that “the difference of twice a number and 3 is 21.” This translates to the equation:
- x
- 3 = 21
where “x” is the unknown number.
Solving for the Variable
To solve for the variable, we need to isolate “x” on one side of the equation. We do this by adding 3 to both sides:
- x
- 3 + 3 = 21 + 3
- x = 24
Now, we divide both sides by 2:
x / 2 = 24 / 2
x = 12Therefore, the value of the unknown number is 12.
Numerical Solution
To verify our solution, we substitute the value of “x” back into the original expression:
- (12)
- 3 = 21
- 24
- 3 = 21
- = 21
The equation holds true, confirming that our solution is correct.
Real-World Application
Understanding the difference between twice a number and 3 can be useful in various real-world situations. For instance, suppose you have a rectangular garden with a length that is twice its width. If the perimeter of the garden is 50 meters, you can use the formula for perimeter (P = 2L + 2W) to solve for the width of the garden, which involves finding the difference between twice the width and the given perimeter.
Query Resolution
What is the first step in solving the equation?
The first step is to assign a variable to represent the unknown number and translate the given information into an algebraic equation.
How do we isolate the variable on one side of the equation?
To isolate the variable, we apply algebraic operations such as addition, subtraction, multiplication, and division, ensuring that the variable remains on one side of the equation while the constant terms are on the other side.
