Equations and Solutions
An Equation is a statement that two quantities are equal.Equations can be as simple asx + 3 = 5 or more complex as 2(x/3 + 1) + 5x = 4x + 12 A solution to an equation in a single variable is a number which when substituted for the variable that makes the statement true.Obviously 2 is a solution to the equation x + 3 = 5 since 2 + 3 = 5 is a true statement.It is less obvious that 6 is a solution to 2(x/3 + 1) + 5x = 4x + 12 since2(6/3 + 1) + 5(6) = 4(6) + 12 2(2 + 1) + 30 = 24 + 12 2(3) + 30 = 24 + 12 6 + 30 = 24 + 12 36 = 36. A systematic procedure for solving equations such as those given above is sometimes referred to as the golden rule of equations. The solution set for an equation is the set of all solutions to the equation.
Equivalent equations are equations with the same solution set.
The following equations are equivalent since both have solutions set, {2}. |
