Table of Contents
- Introduction
- Simple Equations: Definition and Examples
- Solving Simple Equations
- Examples in R Programming
Introduction
Understanding simple equations is a fundamental aspect of algebra. This document aims to introduce the concepts of simple equations, demonstrate how to solve them, and provide practical examples using the R programming language.
Simple Equations: Definition and Examples
A simple equation is a mathematical statement that asserts the equality of two expressions. These equations typically involve a variable, which we solve for.
A simple linear equation: \( ax + b = 0 \)
Where \(a$\)and \(b$\)are constants, and \(x$\)is the variable.
Solving Simple Equations
The goal is to isolate the variable (usually \(x\)) on one side of the equation. This involves applying inverse operations to both sides of the equation to keep the equation balanced.
Addition and Subtraction
To get rid of a number added to \(x\), we subtract the same number from both sides of the equation.
Multiplication and Division
If \(x$\)is multiplied by a number, we divide both sides of the equation by that number.
Examples in R Programming
We can use R to solve simple equations. Below are examples demonstrating this.
Example 1: Solving \( 2x + 3 = 7 \)
# Define the equation
solve_equation <- function(a, b, c) {
(c - b) / a
}
# Solve 2x + 3 = 7
solve_equation(2, 3, 7)
Example 2: Solving \( 5x - 4 = 16 \)
# Solve 5x - 4 = 16
solve_equation(5, -4, 16)