math. algebra
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The document contains examples of word problems involving rates, ratios, mixtures, as well as definitions and properties of linear inequalities, including the transitive, addition, and multiplication properties of inequalities, and examples of solving and graphing linear inequalities and their solution sets. The final part asks students to solve and graph the solution sets of several linear inequalities as seatwork.
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math. algebra
- 1. MATH
- 2. 1. How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution? 40L 50% x L 20% (40+x) L 30%+ =
- 4. 3. Poppy can mow the lawn in 40 minutes and Ryann can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?
- 5. 4. An airplane which travels 180 miles per hour leaves the airport 8.5 hours after a ship sailed. If it overtakes the ship in 1 hour and 30 minutes, find the rate of the ship. RATE TIME DISTANCE Airplane 180mi/h 1.5h 1.5(180) Ship x 1.5h + 8.5h 10x
- 6. 5. A bus traveling at an average rate of?50?kilometers per hour made the trip to town in?6?hours. If it had traveled at?45?kilometers per hour, how many more minutes would it have taken to make the trip? RATE TIME DISTANCE A 50kph 6h 300km B 45kph 6h + x 45(6 + x)
- 7. Linear InequalityAn INEQUALITY is a mathematical statement which states that two quantities are not equal. TRICHOTOMY AXIOM For any numbers x and y, one and only one of the following is true: x < y x > y
- 8. Linear InequalityREMEMBER! < - less than > - greater than ¡Ü - less than or equal to ¡Ý - greater than or equal to ¡Ù - not equal to
- 9. When 3 is added to x, the sum remains larger than 9. Linear InequalityWhen you triple d and subtract 6, the result remains less than or equal to 15.
- 10. Linear Inequality Either s is greater than 8 or less than -8. t is greater than -1 but less than 5.
- 11. Linear Inequality REMEMBER! < or > ---------- ( parentheses ) ¡Ü or ¡Ý ----------
- 12. Linear Inequality x > 4 x ¡Ý 5 8 < x x ¡Ý 7 0 ¡Ü x < 5
- 13. Linear Inequality x < 7 -5 ¡Ý x
- 14. Linear Inequality -5 < x < 7 x > 9 or x < -9
- 17. Linear InequalityAssignment: What are the properties of inequalities used in solving inequalities?
- 18. Linear Inequality 1. TRANSITIVE PROPERTY OF INEQUALITY (TPI) 2. ADDITION PROPERTY OF INEQUALITY (API) 3. MULTIPLICATION PROPERTY OF INEQUALITY (MPI) Properties of Inequality
- 19. Linear Inequality1. TRANSITIVE PROPERTY OF INEQUALITY (TPI) For every x, y, and z , if x < y and¡Ê ? y < z, then x < z. example: If 4 < 9 and 9 < 10, then _______. If 5 > 0 and 0 > -5, then _______.
- 20. Linear Inequality2. ADDITION PROPERTY OF INEQUALITY (API) For every x, y and z, any¡Ê ? number, if x < y, then x + z < y + z. example: If 4 < 9 (z = 2), then _______________. If 5 > 0 (z = -7), then _______________.
- 21. Linear Inequality3. MULTIPLICATION PROPERTY OF INEQUALITY (MPI) For every x, y , if x < y, then¡Ê ? xz < yz if z > 0 or xz > yz if z < 0. example: If 4 < 9 (z = 2), then _______________. If 5 > 0 (z = -7), then _______________.
- 22. Linear InequalityEXAMPLES: 1.2x + 5 > 3x ¨C 3 2.3(x + 2) + 12 ¡Ý 24 3.1 ¡Ü x + 1 < 6 4.2x ¨C 1 > 7 or 2 ¨C 3x ¡Ý -1 {x | x < 11} {x | x ¡Ý 2} {x | 0 ¡Ü x < 5} {x | x > 4} or {x | x ¡Ü 1}
- 23. Linear InequalitySEATWORK: Solve and graph the solution set of each of the following inequalities. Get one whole sheet of paper. :)