Chapter 15: Finding the Unknown
A balance with mystery boxes, a matchstick pattern, a number puzzle: each hides an unknown number. In this chapter we write such situations as equations, solve them step by step by doing the same to both sides, check our answers, spot and mend common mistakes, and meet problems solved by Indian mathematicians centuries ago.
In this chapter you will
- write equations for situations
- solve equations by balancing and undoing
- solve equations with letters on both sides and brackets
- check solutions and correct mistakes
Topics
- Find the Unknowns NCERT P2 7.1
An equation says two expressions are equal; its solution makes it true.
- Solving Equations Systematically NCERT P2 7.2
Undo the operations in reverse order, doing the same to both sides.
- Mind the Mistake, Mend the Mistake NCERT P2 7.3–7.4
Check every solution by putting it back into the equation.
Key words
- Equation
- a statement that two expressions are equal
- Unknown
- the letter whose value we want
- Solution
- the value that makes the equation true
- Balance
- doing the same thing to both sides keeps an equation true
- Coefficient
- the number multiplying the letter, like 3 in 3x
Summary
- An equation is like a balance: do the same thing to both sides.
- Undo operations in reverse order; gather letters on one side and numbers on the other.
- Turn word problems into equations by naming the unknown.
- Check every solution; Brahmagupta: Ax + B = Cx + D gives x = (D − B) ÷ (A − C).