LINEAR EQUATIONS

LINEAR EQUATIONS Algebra LINEAR EQUATIONS This chapter covers solving for unknowns using linear equations. EO 1.2 SOLVE for the unknown given a linear equation. The rules for addition, subtraction, multiplication, and division described in previous lessons will apply when solving linear equations. Before continuing this course it may be worthwhile to review the basic math laws in Module 1 and the first chapter of this module. Solutions to Algebraic Equations The equation is the most important concept in mathematics. Alone, algebraic operations are of little practical value. Only when these operations are coupled with algebraic equations can algebra be applied to solve practical problems. An equation is a statement of equality between two equal quantities. Most people are familiar with the concept of equality. The idea of equal physical quantities is encountered routinely. An equation is merely the statement of this equality. There are three key ideas in an equation: an equation must involve two expressions, the expressions must be equal, and the equation must indicate that the expressions are equal. Thus, the statement that the sum of three and one equals four is an equation. It involves two expressions, (four and the sum of three and one), the expressions are equal, and the equation states that they are equal. The equal sign (=) is used to indicate equality in an equation. In its most general form, an algebraic equation consists of two algebraic expressions separated by an equal sign. The equal sign is the key sign in algebra. It is the sign that defines one expression in terms of another. In solving practical problems, it is the sign that defines the unknown quantity in terms of known quantities. Algebraic Equations There are two kinds of equations: identities and conditional equations. An identity is an equation that is true for all values of the unknown involved. The identity sign (�) is used in place of the equal sign to indicate an identity. Thus, x² � (x)(x), 3y + 5y � 8y, and yx + yz � y(x + z) are all identities because they are true for all values of x, y, or z. A conditional equation is one that is true only for some particular value(s) of the literal number(s) involved. A conditional equation is 3x + 5 = 8, because only the value x = 1 satisfies the equation. When the word equation is used by itself, it usually means a conditional equation. MA-02 Page 4 Rev. 0