Five Times The Difference Of A Number And 3

Unveiling the Equation: Five Times the Enigma of (x – 3)

Have you ever grappled with a mathematical labyrinth, where the elusive value of ‘x’ seems to dance just beyond your grasp? Imagine a realm where ‘x’ dictates the perplexing equation of five times the difference between itself and the enigmatic 3. In this cerebral odyssey, we embark on a quest to decipher this cryptic formula, its elusive solution, and its profound implications.

Navigating the Unknown: Delving into the Depths of (5(x – 3))

As we delve deeper into the intricate tapestry of this mathematical riddle, we encounter countless challenges that test our logical faculties. The enigmatic nature of ‘x’ casts a shroud of uncertainty over the equation, making it an elusive phantom that taunts our understanding. The elusive difference between ‘x’ and the ever-present 3 adds another layer of complexity to this mathematical conundrum, creating a labyrinth of uncertainty that demands our utmost mental agility.

Cracking the Code: Illuminating the Solution to 5(x – 3)

In the face of these formidable obstacles, a ray of clarity emerges. Through diligent exploration and the application of fundamental mathematical principles, we can illuminate the path to the solution. By systematically unpacking the equation, we unravel the intricate web of relationships between ‘x’ and its mysterious companion, 3. The key lies in recognizing the distributive property, which empowers us to expand the expression and reveal the hidden connections within.

Distilling the Essence: Key Points Regarding (5(x – 3))

Our journey through the equation of five times the difference of a number and 3 has illuminated several essential truths:

  • The equation represents a linear expression involving the unknown variable ‘x’.
  • It can be expanded using the distributive property to reveal the relationship between ‘x’ and 3.
  • The solution to the equation can be determined by isolating ‘x’ and applying appropriate algebraic operations.
  • Understanding this equation enhances our problem-solving abilities and strengthens our grasp of mathematical concepts.
Five Times The Difference Of A Number And 3

Five Times the Difference of a Number and 3

Introduction

In the vast expanse of mathematical equations, one expression that often finds its way into calculations is “five times the difference of a number and 3.” This article delves into the intricacies of this expression, providing a comprehensive guide to its understanding and application.

The Expression

The expression “five times the difference of a number and 3” can be written as:

5(x - 3)

Where x represents any real number.

Steps to Evaluate

To evaluate this expression, follow these steps:

  1. Subtract 3 from the given number: x – 3
  2. Multiple the result by 5: 5(x – 3)

Example

If x = 10, then:

5(10 - 3) = 5(7) = 35

Properties

Linear Function: 5(x – 3) is a linear function with a slope of 5 and a y-intercepts of -15.

Even Function: The expression is even, meaning it remains the same when the input is replaced by its negative.

Domain and Range: The domain of the expression is all real numbers, and the range is all real numbers greater than or equal to -15.

Graph

The graph of 5(x – 3) is a straight line with a positive slope.


[Image of graph of 5(x – 3)]
https://tse1.mm.bing.net/th?q=graph+of+5%28x%20-3%29

Intercepts

  • x-intercepts: None
  • y-intercepts: -15

**Algebraic *Manipulation*

Factoring: 5(x – 3) can be factored as:

5(x - 3) = 5x - 15

Expanding: To expand 5(x – 3), use the distributive property:

5(x - 3) = 5x - 15

**Real-World *Application*

Example 1: A farmer has 50 acres of land. She wants to plant corn on 3/5 of her land. How many acres of corn will she plant?

Solution:

5(50 - 3) = 5(47) = 235

Therefore, she will plant 235 acres of corn.

Example 2: A company’s profit is $500,000. Their expenses are 30% of their profit. What is their net profit?

Solution:

5(500,000 - 3) = 5(497,000) = 2,485,000

Therefore, their net profit is $2,485,000.

Conclusion

“Five times the difference of a number and 3” is a fundamental mathematical expression with many applications in real-world problems. By understanding its properties and how to evaluate it, we can effectively solve various mathematical equations.

After the Conclusion

  • Related concepts: Linear functions, factoring, algebraic expressions.
  • Tips for solving: Factor out the expression or use the distributive property.
  • Common mistakes: Forgett

Video Prealgebra – Part 48 (Translate to Algebraic Expressions)