Forming and Solving Equations

Algebra and Sequences

Choose a letter for the quantity you do not know, and state what it represents together with its units
Where two quantities are related, define the simpler one first and build the other from it
- If a second number is 5 more than the first, call them n and n + 5

Phrase	Expression
4 more than a number	n + 4
7 less than a number	n − 7
Three times a number	3n
A number halved	n/2
A number squared, then doubled	2n²

Words signalling each operation: sum, total and increase for addition; difference, less than and decrease for subtraction; product, times and double for multiplication; shared, split and halved for division
Brackets preserve the order the words describe
- "add 1, then multiply by 3" is 3(n + 1), which differs from "multiply by 3, then add 1", which is 3n + 1

Worked example

Turning a sentence into an equation

Ann is 4 years older than Ben. Their ages add to 34. Form an equation and find Ben's age.

Solution:

Name the unknown first, and choose the smaller quantity so the other is written in terms of it
Let Ben's age be b
Ann is 4 years older, so Ann's age is b + 4
Their ages add to 34, which gives the equation b + (b + 4) = 34
Collect: 2b + 4 = 34
Subtract 4: 2b = 30, then divide by 2: b = 15
Ben is 15 years old
Answer the question asked: b = 15 alone is not an answer about ages, and checking gives 15 + 19 = 34