Question

Explain the difference between an equation and an inequality. Write at least two of each, one of the form px+q and one of the form p(x+q), and explain the steps you take to solve.

Answer 1

Answer: One important difference between an equation and an inequality is that if you subtract one side of an equation from the other, you will get 0

In the case of an inequality, if you subtract one side from the other, you will get something other than 0

That’s an important fact about equations and inequalities that is often utilized in finding solutions.

When I was teaching I noticed that students frequently interpreted the =

sign to mean ‘find the answer’. It does not mean that. It only means that the expression on the left hand side has the same value as the expression on the right hand side.

Students who think that =

means ‘find the answer’ become confused when they see symbols like < , ≠

, or ≈

A further issue these days has to do with computational technology.

This issue has to do with variable assignment. In many programming languages, a statement like =+1x1

has the meaning, “Add one to the current value of x

and then reassign that value to x

.” However, the equation =+1x1

has no solution in traditional algebra.

Programming languages that use =

for variable assignment tend to use ==

to mean equality in our traditional math sense.

Though something like the meaning of =

might seem trivial and ‘obvious’ to many people, there’s actually a lot of subtle variations of understanding possible, and it is important to be aware of these nuances, because that is where confusions arise for students.