Two sides and an equal sign
An equation says that two expressions are equal.
Jasmine’s 99 matchsticks
The arrangement at position n has 2n + 1 sticks. Jasmine has exactly 99 sticks and wants to make one arrangement from them.
How can we write “the arrangement at position n has exactly 99 sticks”?
What this lesson covers
The idea
An equation is a statement of equality between two algebraic expressions, written with an equal sign '=' between them; the two sides are its Left Hand Side (LHS) and Right Hand Side (RHS).
Jasmine’s 99 matchsticks
The arrangement at position *n* has 2n + 1 sticks. Jasmine has exactly 99 sticks and wants to make one arrangement from them.
How can we write “the arrangement at position *n* has exactly 99 sticks”?
- 2n + 1
- 2n + 1 = 99
- 2n + 1 + 99
Equation or not?
Look at each card. Is it an equation? If it is, tap its LHS (Left Hand Side) and then its RHS (Right Hand Side).
An equal sign between two expressions
2n + 1 has no equal sign. It is only an expression. 2n + 1 = 99 puts an equal sign between two expressions, so it is an equation.
The LHS is what is before the “=”, and the RHS is what is after it. A number alone is an expression too, so it can be a side (like 20 above).
A statement of equality between two algebraic expressions, with an equal sign “=” between them, is called an equation. Its two sides are the Left Hand Side (LHS) and the Right Hand Side (RHS).
- Equation | LHS | RHS
- 3x + 4 = 7 | 3x + 4 | 7
- 20 = y − 3 | 20 | y − 3
- 2z + 4 = 5z − 14 | 2z + 4 | 5z − 14
Notes
A statement of equality between two algebraic expressions, with “=” between them, is an equation. The two sides are its LHS and RHS.
Check yourself
Which of these is an equation?
In the equation 20 = y − 3, which part is the LHS?
Is 3 = 50 an equation?
In the equation 2z + 4 = 5z − 14, put z = 6 in the RHS 5z − 14. What number do you get?
Answer: 16
5 × 6 − 14 = 30 − 14 = 16. (The LHS 2 × 6 + 4 is 16 as well.)
- 7m − 3. There is no equal sign. This is only an expression.
- 7m − 3 = 25 — correct. Yes! Two expressions with an equal sign between them.
- 7m − 3 + 25. There is no equal sign. This is only a longer expression.
- y − 3. That is the part after the “=”, the RHS.
- y. The LHS is a whole expression before the “=”. The letter *y* is only a part of the RHS.
- 20 — correct. Yes! The LHS is the part before the “=”, even when it is only a number.
- Yes: it has an equal sign between two expressions (numbers are expressions too). — correct. Yes! The book lists it as an equation. It is not true, but an equation is just the statement of equality.
- No: an equation must have a letter-number in it.. Not so. What matters is the equal sign between two expressions. The book lists 3 = 50 as an equation.
- No: the two sides are not equal.. An equation only states equality. Whether the two sides really are equal is a different question: it is what solving finds out.