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An equality and equation are essentially the same thing. The equality between two expressions is represented by an equation (and conversely).
By using the quadratic equation formula or by completing the square
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trial-and-error
foe r mrejg
An equality and equation are essentially the same thing. The equality between two expressions is represented by an equation (and conversely).
By using the quadratic equation formula or by completing the square
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Problem solving consists of using generic or ad hoc methods, in an orderly manner, for finding solutions to problems.
lesson 2 on problem solving. what are common methods for establishing a benchmark?
trial-and-error
foe r mrejg
Methods vary considerably depending upon the number of powers in the equation. For example, the method for solving cubics is quite different to solving quadratics etc... It's not really possible to generalise to one technique.
A line is represented by an equation. Each solution of the equation is a point on the line, and each point on the line is a solution to the equation. So the line is just the graph of the solution set of the equation.
An equation is a ploblem with no answer and an expression is a problem with an answer so you'll get different answers with an equation and an expression.
The difference is that first you have to understand the problem and translate it into an equation (or equations).
The answer depends on the nature of the equation. Just as there are different ways of solving a linear equation with a real solution and a quadratic equation with real solutions, and other kinds of equations, there are different methods for solving different kinds of imaginary equations.