# Algebra, The Beginnings

So let’s leave statistics for a while and return to algebra. This post will be a bit more basic but it illustrates a skill needed when converting word problems to equations. First, a couple of definitions:

An Expression in algebra is basically anything you can write down in algebra without the “equal” symbol. You can think of an expression as either side of an equation. Examples are

${x}^{2}\hspace{0.33em}{+}\hspace{0.33em}{3}{x}\hspace{0.33em}{-}{1}{,}\hspace{0.33em}{2}{a}\hspace{0.33em}{+}\hspace{0.33em}{3}{b}{,}\hspace{0.33em}\frac{{x}\hspace{0.33em}{+}\hspace{0.33em}{1}}{{x}\hspace{0.33em}{-}\hspace{0.33em}{1}}{,}\hspace{0.33em}{5}$

They can be complex with more than one unknown or as simple as a number.

An Equation in algebra is two expressions with an “equal” symbol between them. Examples are

$\begin{array}{l}{{x}^{2}\hspace{0.33em}{+}\hspace{0.33em}{3}{x}\hspace{0.33em}{-}{1}\hspace{0.33em}{=}\hspace{0.33em}{2}{a}\hspace{0.33em}{+}\hspace{0.33em}{3}{b}}\\{\frac{{x}\hspace{0.33em}{+}\hspace{0.33em}{1}}{{x}\hspace{0.33em}{-}\hspace{0.33em}{1}}\hspace{0.33em}{=}\hspace{0.33em}{5}}\\{{y}\hspace{0.33em}{=}\hspace{0.33em}{7}}\end{array}$

So let’s look at creating expressions. In what follows, I am going to write an english phrase and follow that with the equivalent algebraic expression.

Double a number: 2x

One more than a number: x + 1

Half of a number: x/2

Seven less than triple a number: 3x -7

Take 5 more than a number then double it: 2(x + 5)

Other letters can be used to show an unknown number, but x is mostly used. Sometimes more that one unknown is needed:

Cost of 3 pears that cost each: 3p

Cost of 7 apples that cost a each: 7a

Total cost of the above fruit: 3p + 7a

The individual price 3 people pay at a restaurant if they split the bill: C/3

The total number of pencils in a classroom if each girl has 3 pencils and each boy has 2: 3g + 2b

It is usually a good practice to break down a word problem and write down the expressions first before generating an equation.

Let’s look at creating equations in my next post.