Introduction
An equation is a mathematical statement that shows two expressions are equal using an equal sign (=). Linear equations in one variable involve only one unknown letter, like 'x' or 'y', with a power of 1.
Explanation Step by Step
To solve an equation, isolate the variable on one side. Use the "Inverse Operation" method: if a number is added, subtract it from the other side; if multiplied, divide it.
Sub-topics
Equations in one variable and word problems
Word problems translate real-life situations into mathematical equations to find unknown values.
Examples
Example 1: Basic Solving
Example 2: Shopping Scenario (Real-life)
Aarav bought 3 identical notebooks and paid 90 rupees. What is the cost of one notebook?
Tricky Example
The sum of three consecutive integers is 33. What is the smallest integer?
Tricks and Shortcuts
- The "Transpose" Rule: Moving a term across the '=' sign flips its sign (+ to -).
- Always plug your answer back into the original equation to check if LHS = RHS.
Common Mistakes
- Adding a number to one side but forgetting to add it to the other.
- Incorrectly distributing a negative sign inside brackets.
Practice Questions
Easy Questions
- Solve for y: y + 12 = 30.
- If you double a number and get 40, what is the number? (Real-life)
- Tricky: Solve 5 - x = 2. (Watch the sign of x!)
Medium Questions
- Solve: 2(x - 5) = 10.
- A father is 28 years older than his son. Their total age is 48. Find the son's age. (Real-life)
- Tricky: Solve x/4 + 7 = 10.
Hard Questions
- The perimeter of a garden is 100m. The length is 10m more than the width. Find the dimensions. (Real-life)
- Find a number such that 1/4 of it is 2 more than 1/5 of it.
- Tricky: A bus travels with some passengers. At the first stop, half get down and 5 enter. Now there are 25. How many were there initially?
Revision Summary
Equations help solve unknowns. Remember to keep the equation balanced. Practice converting words into symbols carefully to master word problems.