Mathematics 101
- Reminder of Fundamentals
- Advanced Arithmetics
- Introduction to Geometry
- In-depth Geometry
- Deeper into Numbers
- Further into Algebra
- Elementary Statistics & Probability
- Advanced Statistics, Probability
- Mathematical Logic
- Calculus
- Calculus
- Trigonometry I
- Trigonometry II & Conclusion
Reminder of Fundamentals
Understanding and Solving Simple Equations
Basic concepts of algebra of the real and complex numbers.
Introduction
Equations are fundamental to mathematics. They are statements that assert the equality of two expressions. In simple terms, an equation is like a balance scale. Whatever you do on one side of the scale (or equation), you must also do on the other side to keep it balanced.
Understanding the Concept of Variables
In mathematics, a variable is a symbol used to represent an unknown or arbitrary number. The most common symbols used as variables in equations are x, y, and z. For example, in the equation x + 2 = 5, 'x' is a variable.
Forming Simple Equations
Forming simple equations can be a useful skill in solving problems. For example, if you know that the sum of two numbers is 10 and one of the numbers is 2, you can form the equation x + 2 = 10 to find the other number.
Solving Simple Equations
Solving an equation means finding the value of the variable that makes the equation true. Here are the basic steps to solve a simple equation:
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Simplify the equation: Combine like terms on each side of the equation. For example, in the equation 2x + 3 + x = 10, you can combine the '2x' and 'x' to get '3x', so the equation becomes 3x + 3 = 10.
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Isolate the variable: Get the variable on one side of the equation and the numbers on the other side. In the above example, you can subtract 3 from both sides of the equation to get 3x = 7.
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Solve for the variable: Divide both sides of the equation by the coefficient of the variable to solve for the variable. In the above example, you can divide both sides by 3 to get x = 7/3.
Practical Applications of Simple Equations
Simple equations are used in many real-life situations. For example, if you are shopping and you know the total amount you want to spend and the cost of each item, you can use a simple equation to find out how many items you can buy. Or if you are saving money for a big purchase, you can use a simple equation to figure out how much you need to save each month.
In conclusion, understanding and solving simple equations is a fundamental skill in mathematics. It forms the basis for more complex equations and mathematical concepts.