what is algebra?

Basically algebra is where you use letters (pronumerals ) in place of numbers.  

You use numbers as well.

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for example

In primary school you might have a problems like

$$3+\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}} =75\\\\$$

 

You would have to work out the answer which is 72 and write 72 in the box.

or if the box  was too little to write in maybe you could say  $$\fbox{\begin{minipage}{0.2cm}\hfill\vspace{0.2cm}\end{minipage}} =72$$

In high school you will use letters (pronumerals) instead of boxes.

So the question might be

3+Y=75

and the answer is  Y=72