What do two straight vertical lines mean around a variable in algebra?

Answer 1

Well, it my experience I would say that it mean absolute value bars, which basically means distance from zero. So if I were to find the root of 9 (√9) it would become |3|, which is ± 3 (3 and (-3)).

There's a good definition in the link below.

Here is a possible definition: |x| = √a2

Further reading: If you were to graph the function y=|x| than it will take on a shape of a V, the domain being {xeR} and the range being {y≥ 0, yeR}. If you were to have the point (1,1) on the graph you should have the corresponding point (-1,1) on the other side (since the root of x2 (√x2) is |x| which can be broken down into ± x (x and -x) thus the points being (-x,y) and (x,y)). the main points to use are (1,1), (0,0) and (-1,1) when sketching transformations. furthermore the inverse is not a function (since there be 2 y points for a given x point, (the graph shape being a < )) and you will need to restrict its domain to make it a function.

Now if you were talking about vectors the bars usually will mean something else, usually being involved in dot and cross product (refer to possible definition). Ex: |x| = √a2 + b2 + c2 , where x is a vector in 3 dimensions.

Including when putting "the bars" around a vector it identifies it as the magnitude only (a vector is magnitude and direction, hence no direction).

Also your high school teacher may do to show that the lines are parallel (but it shouldn't be around a variable).

Original answer: Absolute value