# Confused in how to insert a slack variable in a constraint inequality

According to my understanding, we should put a slack variable to equate an inequality constraint by inserting the slack variable in the side that is less than the other side. For example, if we have $$4x+2<2$$ this will be $$4x+2+\text{slack_variable}=2$$.

But in the example section of the Slack Variable Wikipedia, it says the following:

By introducing the slack variable $$y\ge0$$, the inequality $$Ax\le b$$ can be converted to the equation $$y-Ax+b = 0$$.

Which means that the slack variable is inserted on the bigger side! Please someone explain this confusion.

• The Wikipedia example is wrong. It should be $Ax+y=b$. Apr 7 '20 at 3:20
• FYI, I just fixed the Wikipedia entry. Apr 7 '20 at 22:15
• Many thanks for all of you . Apr 7 '20 at 22:52