Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
ALGEBRA II. NOTES SECTION 2.1 SOLVING INEQUALITIES IN ONE VARIABLE In the last chapter, we worked with solving equations in 1 variable: Ex.) 2x 3 17 What if we replace the equals sign with an inequality symbol? How is our solution affected? Ex.) 2x 3 17 Note: 1.) use an open circle when graphing inequalities containing < or >. 2.) use a closed circle when graphing inequalities containing or . So to solve inequalities, we’re basically doing the same steps as the ones used in solving equations with 1 exception: Multiplying or dividing by a negative: Ex.) 6x 12 A.) STEPS TO SOLVE INEQUALITIES: 1.) Simplify both sides. 2.) Add to or subtract from both sides. 3.) Multiply or divide each side by a nonzero #. (If multiplying or dividing by a negative, switch the inequality.) B.) Equivalent Inequalities – transformations that produce inequalities with the same solution set. Ex.) 2 x 14 and x 7 C.) PROPERTIES OF ORDER – Let a, b, and c be real #’s. 1.) Comparison Property – exactly 1 of the following statements is true: a b, a b, a b . 2.) Transitive Property – If a b and b c , then a c . 3.) Addition Property – If a b , then a c b c . 4.) Multiplication Property – a.) If a b and c is positive, then ac bc . b.) If a b and c is negative, then ac bc . Oral Exercises: pgs. 61–62 #5-17 Sample Problems: pgs. 62-63 12.) 3t 6t 12 18.) 4s 3(2 3s) 5(2 s) 22.) 2 t (2 3t ) 5t 2(1 t ) 3