Basic algebra is essentially advanced arithmetic, therefore much of the terminology and many of the rules are common to both areas. The major difference is that in algebra variables are introduced, which allows us to solve problems using equations and inequalities.
Algebraic expressions are used to describe combinations of letters (variables) and numbers. One way to work with algebraic expressions is to think of them as functions.
We say that equation defines the function f, and the output is called the value of the function corresponding to the input x. Every algebraic expression concludes the coefficient of variable part and the constant term and the terms with the same variable part can be combined.
A statement that equates two algebraic expressions is called an equation.
To solve a linear equation is one variable means to find the value of variable that makes the equation true. Two equations that have the same solution are said to be equivalent. There are two basic rules to help solving linear equations that whether the same constant is added or an equation are multiplied or divided by the same nonzero constant, the quality is preserved, and the new equation is equivalent to the original.
To solve linear equations in tow variables, it is necessary to have two equations that are not equivalent, in another word to solve such a system of simultaneous equations. The only way to resolve them is to eliminate one variable.
A quadratic equation is any equation containing quadratic variable. Such equation can always be solved by the formula or more quickly by factoring.
Any mathematical statement that uses symbols (≠, ≤, ≥, <, > )is called an inequality. The solutions dissemble of equation is that while both sides of the inequality multiplied (or divided) by the same constant, the direction of inequality is preserved if the constant is positive, but reserved if the constant is negative.
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