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Solving Inequalities

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

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Solving Inequalities

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  1. Solving Inequalities Algebra 1

  2. 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

  3. 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

  4. Please complete the following questions for homework tomorrow.

  5. Solve. m - 3 < 6

  6. Answer: m<9~add 3 to both sides

  7. Solve. 3 + a < 6

  8. Answer: a<3~subtract 3 from both sides

  9. Solve. -2 > x - 3

  10. Answer: x<1 ~add 3 to both sides

  11. Solve. t + (-3) > -4

  12. Answer: t >-1 ~Add 3 to both sides

  13. Solve. 3 + y < -2

  14. Answer: y<-5 ~Subtract 3 from both sides

  15. Solve. 2x < -8

  16. Answer: t<-4 ~Divide 2 from each side

  17. Solve. 12 > 6k

  18. Answer: k<2 ~Divide by 6 on both sides

  19. Solve.

  20. Answer: a>6~Multiply by -3 on both sides, flip the inequality sign

  21. Simplify.

  22. Answer: a>-10~Multiply each side by 5, then divide each side by 2

  23. Solve.

  24. 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

  25. Solve. 3x - 1 > 5

  26. Answer: x>2~Subtract 1 from each side, then divide each side by 3

  27. Solve. -2n + 3 < 7

  28. Answer: n>-2Subtract 3 from each side then divide each side by a -2, switch the inequality sign because we are dividing by a negative number

  29. Solve. 8 < 2 - 3r

  30. Answer: r<-2~Subtract 2 from each side then divide by -3, switch the inequality sign because we are dividing by a negative number

  31. Solve.

  32. 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

  33. Solve.

  34. Answer: x<-7Multiply each side by 5, then subtract 2 from each side

  35. Write an inequality: A number is greater than -3.

  36. Answer: n<-3

  37. Write an inequality: 2 less than a number is less than 9.

  38. Answer: n-2<9

  39. Helpful Websites • http://www.youtube.com/watch?v=VgDe_D8ojxw • http://www.mathsisfun.com/algebra/inequality-solving.html • http://www.webmath.com/solverineq.html

  40. 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.

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