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Solving Inequalities

Solving Inequalities. -5 0 5. Solve the inequality 10 + y  12 then graph the solution. Solution: 10 + y  12 -10 -10 subtract 10 from both sides y  2. -10 0 10.

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Solving Inequalities

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  1. Solving Inequalities

  2. -5 0 5 Solve the inequality 10 + y  12 then graph the solution. Solution: 10 + y  12 -10 -10 subtract 10 from both sides y  2

  3. -10 0 10 Solve the inequality 7.6  t – 2.4 then graph the inequality. Solution: 7.6  t – 2.4 +2.4 +2.4 add 2.4 from both sides 10  t or t  10 Note: reverse the inequality symbol when switching position.

  4. Do these… Solve each inequality. Then graph the solution. 1. d – 13  -8 2. 3.2  r + 4.7 Answers: 1. d  5 2. -1.5  r or r > -1.5

  5. Solve each inequality. 1. 4x + 3 < 11 Solution: 4x + 3 < 11 -3 -3 subtract 3 form both sides 4x < 8divide both sides by 4 4 4 x < 2 Note: to avoid confusion in solving inequalities, ALWAYS PUT VARIABLES ON THE LEFT SIDE

  6. 2. 2(3f +2) > 14f + 12 Solution: 2(3f +2) > 14f + 12 6f + 4 > 14f + 12 distribute 2 -4 -4 subtract 4 from both sides 6f > 14f + 8 -14f -14f subtract 14f from both sides -8f > 8 divide -8 from both sides f < -1 Note: when dividing or multiplying both sides by a negative number, REVERSE THE INEQUALITY SYMBOL

  7. Do these… Solve each inequality. Graph and check your solution. 1. 1.5 + 2.1y < 1.1y + 4.5 2. 4(n + 3)  3(2n + 8) Answers: 1. y < 3 2. n  -6

  8. Write and solve an inequality that models each situation. • Ernest works in the shipping department loading shipping crates with boxes. Each empty crate weighs 150 lb. How many boxes, each weighing 35 lbs, can Ernest put in the crate if the total weight is to be no more than 850 lbs? Solution: Let x = no. of boxes 35lbs. = weight of each box Relate: 35 lbs times no. of boxes plus weight of empty crateis no more than 850 lbs. 35x + 150  850

  9. Cont.. 35x + 150  850 35x  700 subtract 150 from both sides x  20 divide both sides by 35 Ernest can put 20 boxes or less, each weighing 35 lbs in the crate.

  10. 2. Beatriz is in charge of setting up a banquet hall. She has five tables that will seat six people each. If no more than 62 people will attend, how many tables seating four people each will she need? Solution: Let x = no. of tables for four people Relate: Five tables times six people plus four times no. of tables is no more than 62 5(6) + 4x  62 5(6) + 4x  62 30 + 4x  62 4x  32 subtract 30 from both sides x  8 divide both sides by 4 Beatriz needs 8 tables.

  11. 3. The cost to rent a car is $19.50 plus $.25 per mile. If you have $44 to rent a car, what is the greatest number of miles that you can drive? Solution: Let x = no. miles you can drive Relate: 19.50 plus .25 times no. of miles is less than or equal to 44. 19.50 + .25x 44 .25x  24.5 subtract 19.50 from both sides x  98 divide .25 from both sides The greatest number of miles that you can drive is 98 miles.

  12. Do these… • Suppose it costs $5 to enter a carnival. Each ride costs $1.25. You have $15 to spend at the carnival. What is the greatest number of rides that you can go on? • The student council is sponsoring a concert as a fund raiser. Tickets are $3 fro students and $5 for adults. The student council wants to raise at least $1000. If 200 students attend, how many adults must attend? Answers: 1. x 8, you can go up to 8 rides 2. x 80, their should be 80 adults or more

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