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Unformatted text preview: PreCalculus Section P.7 Equations Linear Equation in One Variable equation that can be written in the form = + b ax where b a , are real numbers and a examples: 5 3 2 , ) 3 ( 5 , 13 2 = = = + x x x Solving an equation in x determine all values of x that result in a true statement when substituted into the equation these values are known as solutions or roots these values are also said to satisfy the equation solution set set of all values that satisfy the equation; use braces {} to denote a set example: the solution set of 14 2 = x is { } 7 equivalent equations two or more equations that have the same solution set example: 7 , 14 2 , 14 2 = = = x x x are equivalent equations that have the same solution set of { } 7 Generating Equivalent Equations 1. Simplify by removing grouping symbols and combining like terms. 2. Add/Subtract the same expression from BOTH sides of the equation. 3. Multiply/Divide by same nonzero expression on BOTH sides of the equation. 4. Switch the two sides of the equation. Example to be done on board. To Solve Linear Equation 1. Simplify both sides of the equation by removing grouping symbols and combining like terms. 2. Collect all the variable terms on one side of the equation and constant terms on the other side. 3. Isolate the variable and solve. 4. Check solution in original equation. EX 1: Solve ) 5 2 ( 3 29 ) 1 2 ( 4 + = + x x Equations with Fractions To solve equations with fractions multiply each term on both sides of the equation by the least common denominator (LCD) then proceed as earlier. EX 2: Solve 7 5 14 5 4 3 + = x x Rational Equations equation containing one or more rational expressions examples of rational equations: 7 1 21 5 3 , 1 6 1 1 1 3 2 + = = + x x x x x If the variable occurs in the denominators of any terms in the rational equation, the values that would make those denominators zero must be excluded as possible solutions. example: For the equation 10 3 8 5 4 2 1 2 = + + x x x x , 5 2  x and x since they would result in at least one of the denominators being zero. Note: ) 2 )( 5 ( 10 3 2 + = x x x x Note: When solving an equation if you get x equal to one of the restrictions, the equation has no solution, denoted by EX 3: Solve 6 20 2 5 3 6 2 + = + x x x x Solving a formula for a variable Get the variable you are solving for isolated on one side of the equation. EX 4: Solve for 1 f : 2 1 2 1 1 f f f f f + = Equations Involving Absolute Values Rewriting an absolute value equation without the absolute value bars If c is a positive real number and u represents any algebraic expression, then c u = is equivalent to c u = or c u = To Solve an Absolute Value Equation 1 st isolate the absolute value on one side of the equation. Then rewrite the equation without the absolute value bars and solve the resulting equations. Check your solutions in the original equation.Check your solutions in the original equation....
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This note was uploaded on 11/23/2010 for the course MATH 115 taught by Professor Mcbride,v during the Fall '08 term at University of South Dakota.
 Fall '08
 Mcbride,V
 Calculus, PreCalculus, Real Numbers, Equations

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