1. Name:________________________________________________________________________________Date:_____/_____/__________ 1) x –(-4) = -102) -6x = 60 4) 3x + 2 = 175) 11 = -9x – 7 Solve the following 1-step equations: Solve the following 2-step equations: Solve the following miscellaneous “fraction” 2-step equations:

2. Today’s Lesson: What: Inequalities Why: To identify and graph inequalities. What: Inequalities Why: To identify and graph inequalities.

3. What is an inequality?? An inequality is a math sentence that describes two or more quantities that are _______ equal. In other words, the left and right sides of the inequality are NOT __________________. inequality symbols... NOT balanced

4. Real-life examples... Consider the following signs: If x represents speed... 1) Inequality for obeying the speed limit: _________________________________ 2) Inequality for not obeying the speed limit: _________________________________ What does an inequality have to do with real life?? x ≤ 55 x > 55

5. Real-life examples... If x represents height... 3) Inequality for being able to ride: _____________________________ 4)Inequality for not being able to ride: ____________________________ 48” x ≥ 48 x < 48

6. Real-life examples... If x represents age... 5) Inequality for eating free: _____________________________ 6) Inequality for not eating free: ____________________________ x ≤ 10 x > 10

7. What does it mean?? In an equation, the variable (x) represents ONE number. Is this true in an inequality?? Consider the following inequalities... 1) x > 25 Meaning: 2) x ≤ 6 Meaning: 3) x < 10 Meaning: 4)x ≥ 12 Meaning: x is ALL numbers BIGGER than 25. x is ALL numbers SMALLER OR EQUAL to 6. x is ALL numbers SMALLER than 10. x is ALL numbers BIGGER OR EQUAL to 12.

8. Circle EVERY number that could be a solution to the following inequalities : 1) x ≥ -6 0-6-6.5-76 for the test... 2) x < -3 0-3.5-5-3-2

9. graphing an inequality... Open or Closed Circle?? When graphing the answer to an inequality on a number line, we use an __________________ circle for > or < signs, and a ______________________ circle for ≥ or ≤ signs. How can you remember that? Here’s a little trick: DOES THE BIRD GET THE WORM ?!? If the bird “gets the worm,” his belly is full, so we use a ____________________________ circle. If the bird does NOT get the worm, his belly is empty, so we use an _________________________ circle. open closed closed ( ) open ( )

10. Graph the following inequalities on the given number lines: 1) x ≥ -4

11. 2) x < -4 3) x > -1 4) x ≤ 2

12. What about when “x” is on the right side of the inequality?? Consider the following: 4 > x Use common sense: If 4 is greater than x, then x must be LESS than 4 ! If your age is greater than your sister’s age, then your sister’s age must be _____________ than your age! Makes sense. So, in order to reduce careless mistakes, we should re-write the inequality, placing “x” on the LEFT side. HOWEVER, remember to also switch the sign!! Let’s practice... x < 4 Graph the following inequalities on the given number lines (re-write first): 1) 5 ≥ x x ≤ 5 less

13. 2) 0 < x 3) 7 > x x > 0 x < 7

14. END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow represent the homework assigned for that day.

15. Math-7 NOTES DATE: ______/_______/_______NAME: What is an inequality?? What: Inequalities Why: To identify and graph inequalities. What: Inequalities Why: To identify and graph inequalities. An inequality is a math sentence that describes two or more quantities that are _______ equal. In other words, the left and right sides of the inequality are NOT __________________. inequality symbols... Real-life examples... Consider the following signs: If x represents speed... 1)Inequality for obeying the speed limit: ______________________ 2)Inequality for not obeying the speed limit: _________________ If x represents height... 3)Inequality for being able to ride: _____________________________ 4)Inequality for not being able to ride: ________________________ If x represents age... 5)Inequality for eating free: _____________________________________ 6)Inequality for not eating free: ________________________________ 48” What does it mean?? In an equation, the variable (x) represents ONE number. Is this true in an inequality?? Consider the following inequalities... 1) x > 25 Meaning:2) x ≤ 6 Meaning: 3) x < 10 Meaning:4) x ≥ 12 Meaning:

16. Circle EVERY number that could be a solution to the following inequalities : 1) x ≥ -6 2) x < -3 0-6-6.5-760-3.5-5-3-2 for the test... graphing an inequality... Open or Closed Circle?? When graphing the answer to an inequality on a number line, we use an _________________________ circle for > or < signs, and a __________________________ circle for ≥ or ≤ signs. How can you remember that? Here’s a little trick: DOES THE BIRD GET THE WORM ?!? If the bird “gets the worm,” his belly is full, so we use a ____________________________ circle. If the bird does NOT get the worm, his belly is empty, so we use an _________________________ circle. Graph the following inequalities on the given number lines: 1)x ≥ -4

17. 2) x < -4 3) x > -1 4) x ≤ 2 What about when “x” is on the right side of the inequality?? Consider the following: 4 > x Use common sense: If 4 is greater than x, then x must be LESS than 4! If your age is greater than your sister’s age, then your sister’s age must be _____________ than your age! Makes sense. So, in order to reduce careless mistakes, we should re-write the inequality, placing “x” on the LEFT side. HOWEVER, remember to also switch the sign!! Let’s practice... Graph the following inequalities on the given number lines (re-write first): 1)5 ≥ x 2) 0 < x 3) 7 > x

18. Math-7 homework Directions: Write an inequality for the following real-life situations: Directions: Circle EVERY number that could be a solution to the following inequalities (remember to re-write the inequality if x appears on the right side): 7. x > -6 -5-6-7-6.5-5.5 Name: _____________________________________________________________________________ Date: _____/_____/__________ 1.In the U.S., one must be at least 18 years of age in order to vote. If x represents age, write an inequality for people who are able to vote. 2.Driving through old-town Leesburg, the speed limit is 25 mph. If x represents speed, write an inequality for those who are NOT speeding. 3.At Hershey Park, one must be at least 52 inches tall in order to ride the Fahrenheit rollercoaster. If x represents height, write an inequality for those people who are allowed to ride. 4.In order for a car’s air bags to be activated, a passenger must weigh a minimum of 90 lbs. If x represents weight, write an inequality for when the air bags will NOT be activated. 5.You are instructed to spend no more than $50 at the mall. If x represents money, write an inequality for how much money you are allowed to spend. 6.The cheapest entrée at a certain restaurant is $12. If you buy 2 entrees, write an inequality that represents the minimum amount of money you spent (let x represent money). 8. x ≤ 13 120131413.5 9. 3 > x 133.504 11. 15 < x 1015201414.5 10. x ≥ -20 -20-1000-55 12. x ≤ -10 -90-10.5-1,000-10

19. Match each inequality with its graph: Does the bird get the worm? Math-7 homework Name: _____________________________________________________________________________ Date: _____/_____/__________