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Solving Inequalities Algebra 1 • Solving inequalities is similar to solving linear equations (ex. 2x+2=4), except for one small but important detail: you flip the inequality sign whenever you multiply or divide the inequality by a negative number. • Examples -2x=4, answer: x=-2 -2x≥4, answer: x≤-2 Remember: ~The opposite of addition is subtraction ~The opposite of subtraction is addition ~The opposite of multiplication is division ~The opposite of division is multiplication ~When multiplying or dividing by a negative number, the sign of the inequality switches Please complete the following questions for homework tomorrow. Answer: m<9 ~add 3 to both sides Answer: a<3 ~subtract 3 from both sides Answer: x<1 ~add 3 to both sides Answer: t >-1 ~Add 3 to both sides Answer: y<-5 ~Subtract 3 from both sides Answer: t<-4 ~Divide 2 from each side Answer: k<2 ~Divide by 6 on both sides a 2 3 Answer: a>6 ~Multiply by -3 on both sides, flip the inequality sign 2a 4 5 Answer: a>-10 ~Multiply each side by 5, then divide each side by 2 2 6 x 3 Answer: a<-9 ~Multiply each side by 3, then divide each side by -2, switch the inequality sign because we are dividing by a negative number Answer: x>2 ~Subtract 1 from each side, then divide each side by 3 Answer: n>-2 Subtract 3 from each side then divide each side by a -2, switch the inequality sign because we are dividing by a negative number Answer: r<-2 ~Subtract 2 from each side then divide by -3, switch the inequality sign because we are dividing by a negative number x 1 2 3 Answer: x<-3 ~Subtract 1 from each side, then multiply each side by -3, switch the inequality sign because we are multiplying by a negative number x (2) 1 5 Answer: x<-7 Multiply each side by 5, then subtract 2 from each side Answer: n<-3 Answer: n-2<9 Helpful Websites • http://www.youtube.com/watch?v=VgDe_D8o jxw • http://www.mathsisfun.com/algebra/inequalit y-solving.html • http://www.webmath.com/solverineq.html SOL Regulations • A.5 The student will solve multistep linear inequalities in two variables, including • a) solving multistep linear inequalities algebraically and graphically; • b) justifying steps used in solving inequalities, using axioms of inequality and • properties of order that are valid for the set of real numbers and its subsets; • c) solving real-world problems involving inequalities; and • d) solving systems of inequalities.