LINEAR EQUATIONSAlgebraLINEAR EQUATIONSThis 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 willapply when solving linear equations. Before continuing this course it may be worthwhile toreview the basic math laws in Module 1 and the first chapter of this module.SolutionstoAlgebraicEquationsThe equation is the most important concept in mathematics. Alone, algebraic operations are oflittle practical value. Only when these operations are coupled with algebraic equations canalgebra be applied to solve practical problems.An equation is a statement of equality between two equal quantities. Most people are familiarwith the concept of equality. The idea of equal physical quantities is encountered routinely. Anequation is merely the statement of this equality. There are three key ideas in an equation: anequation must involve two expressions, the expressions must be equal, and the equation mustindicate that the expressions are equal. Thus, the statement that the sum of three and one equalsfour is an equation. It involves two expressions, (four and the sum of three and one), theexpressions 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, analgebraic equation consists of two algebraic expressions separated by an equal sign. The equalsign 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 knownquantities.AlgebraicEquationsThere are two kinds of equations: identities and conditional equations. An identity is an equationthat is true for all values of the unknown involved. The identity sign () is used in place of theequal sign to indicate an identity. Thus, x^{2}(x)(x), 3y + 5y 8y, and yx + yz y(x + z) are allidentities because they are true for all values of x, y, or z. A conditional equation is one that istrue only for some particular value(s) of the literal number(s) involved. A conditional equationis 3x + 5 = 8, because only the value x = 1 satisfies the equation. When the word equation isused by itself, it usually means a conditional equation.MA-02 Page 4 Rev. 0

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