7 Maths 4 Simple Equation Part 2

Created Feb. 7, 2024 by Peeyush Kumar

Review of what we know

Variable:

A variable is a letter or a symbol we are using to represent a unknown number. Mathematicians usually choose to name each unknown with just a single letter, mostly out of a need for shortness, since writing one letter is easier than writing a word.

E.g.: They are denoted by any alphabets like x, y, z, a, b, p, l, m...

Source: http://en.wikibooks.org/wiki/Algebra/Variables#Variables_and_Constants

Video: The introduction to variables and variable expressions is explained in the following video

Source:

Expression:

An expression is a collection of symbols you could put into a calculator and get a number. To be precise, an expression is a well formed formula.

E.g.: Linear expressions: 3x+6, 4y-2

Phrase	Expression
six increased by a number x	6 + x
fourteen decreased by a number p	14 - p
five less than a number t	t - 5
the product of 15 and a number n	15 · n or 15n
Forty-three divided by a number y	43 ÷ y

Source: http://en.wikipedia.org/wiki/Expression_(mathematics)

Source for examples: Bhargavi Ramani, 12 June 2013, Examples, Explains how to write expressions.

Writing more basic expressions is best explained in the following videos

Video: http://www.youtube.com/watch?v=SRRgpq4a-zU

Video: http://www.youtube.com/watch?v=-b1pKedxCeo

Equation:

Now (I) and (II) are called Equations.

Equation refers to a relation between some variables that is expressed by the equality of some expressions of their values.

E.g.1

Sentence	Algebraic Equation
A number increased by nine is fifteen.	y + 9 = 15
Twice a number is eighteen.	2n = 18
Four less than a number is twenty.	x - 4 = 20
A number divided by six is eight.	k/6=8

E.g.2:

Sentence	Algebraic Equation
Twice a number, decreased by twenty-nine, is seven.	2t - 29 = 7
Thirty-two is twice a number increased by eight.	32 = 2a + 8
The quotient of fifty and five more than a number is ten.	50/(n+5)=10
Twelve is sixteen less than four times a number.	12 = 4x - 16