Chapter focus
An equation states that two expressions have equal value. Finding the unknown means preserving that equality while undoing operations step by step.
These original explanations support the named Ganita Prakash Part II chapter. Use the full NCERT lesson and exercises for its prescribed methods.
1. An equation is a balance
The left-hand side and right-hand side of an equation have equal values. If the same number is added to, subtracted from, multiplied by or divided into both sides (division only by a non-zero number), equality is preserved.
Think of a balance scale: removing the same weight from both pans keeps the balance level. Do the same operation to both sides, rather than moving a term and changing its sign without explanation.
2. Solve one-step and two-step equations
Worked example: 3x + 5 = 20
- Subtract 5 from both sides: 3x = 15.
- Divide both sides by 3: x = 5.
- Check in the original: 3(5) + 5 = 20.
Worked example: x/4 − 2 = 5
Add 2 to both sides: x/4 = 7. Multiply both sides by 4: x = 28. Check: 28/4 − 2 = 5.
3. Translate words into an equation
Let the unknown be x, then translate each operation in order. “Five less than twice a number is 17” becomes 2x − 5 = 17, not 2(x − 5) = 17. Solve: 2x = 22, x = 11. Check: twice 11 is 22; five less is 17.
Define what the variable represents, include units if the unknown is a measurement, and check that the answer fits the original wording.
Common errors to avoid
- Apply an operation to both sides to preserve equality.
- “Five less than twice x” is 2x − 5; subtraction order matters.
- Do not divide by zero.
- Substitute the final value into the original equation to check.
Practice: set up, solve and check
1. Solve x + 9 = 24.
Answer: Subtract 9 from both sides: x = 15.
2. Solve 4y = 36.
Answer: Divide both sides by 4: y = 9.
3. Solve 5n − 7 = 18.
Answer: 5n = 25, so n = 5. Check: 25 − 7 = 18.
4. Three times a number plus 4 is 25. Find the number.
Answer: 3x + 4 = 25; 3x = 21; x = 7.
5. A number divided by 6 is 8. What is the number?
Answer: x/6 = 8, so x = 48.
Chapter summary
Equations express equality. Use inverse operations on both sides to isolate the unknown, translate word problems in the order described and check every solution in the original equation.