Topic
Equations 4.
Here, there are some unknowns on both sides of the equation, and now we learn to rearrange (group) them on one side. Then we learn about the concepts of identities and inequalities. Finally, we learn how to expand brackets in the equations and trace it back to grouping.
If there are unknown terms with positive signs on both sides of the equation, then move the smaller coefficient to the other side by subtracting it. If there was a constant term on the other side, then move that to the place of the unknown term.
If there are unknown terms with negative signs on both sides of the equation, then move the higher coefficient by adding it to the to the other side. If there was a constant term on the other side, then move that to the place of the unknown term.
If there is an unknown term with a positive sign on one side and a negative sign on the other side of the equation, then move the term with the negative sign by adding it to the other side. If there was a constant term on the other side, then we move that to the place of the unknown term.
If the terms on both sides of the equation are the same, then the equation holds for any values of the unknown. This case is called ‘identity’.
If there is a constant on both sides of the equation and they have got different values, then the equation does not hold for any values of the unknown. This is called ‘inequality’. Hence, the equation has no solution.
If a multi-term expression is in brackets on one side of the equation, then we expand the brackets.
If there are multi-term expressions on both sides of the equation, and both are in brackets, then we expand the brackets.