Do Now 10518 Take out HW from last

Do Now 10/5/18 Ø Take out HW from last night. Text p. 58, #6 -18 evens, 41 -44 all (11 problems) Text p. 65, #8 -32 multiples of 4 (7 problems) Text p. 71, #4 -28 multiples of 4 (7 problems) Ø Copy HW in your planner. Text p. 77, #4 -34 evens – Quiz sections 2. 1 -2. 4 Tuesday – 10/10 Ø Go. Formative and complete the warm-up.

Homework Text p. 58, #6 -18 evens, 41 -44 all

Homework Text p. 65, #8 -32 multiples of 4

Homework Text p. 65, #8 -32 multiples of 4

Homework Text p. 71, #4 -28 multiples of 4

Homework Text p. 71, #4 -28 multiples of 4

Learning Goal SWBAT write, graph, and solve linear, compound, and absolute value inequatilies Learning Target Ø SWBAT graph and solve multi-step inequalities and inequalities with variables on both sides

Section 2. 4 “Solve Multi-Step Inequalities” INEQUALITIES – mathematical sentence formed by placing a <, ≤, >, or ≥ between two expressions. 13 2 1 < 8 2 y – 3 z * 2 2 ≥ 1 4 - z 5 c + 1 4 > 30 11 w - 10 ≤ 121 + 3 w

Section 2. 4 “Solve Multi-Step Inequalities” The steps for solving two-step and multi-step equations can be applied to linear inequalities. Solving Multi-Step Inequalities STEP 1 - Use distributive property and combine like terms. STEP 2 - Collect variables on one side of the inequality. STEP 3 - “Undo” addition and/or subtraction. STEP 4 - “Undo” multiplication and/or division. (If multiplying or dividing by a negative, flip the inequality sign). STEP 5 - Solve for the variable. STEP 6 - Check your work. STEP 7 - Graph your solution

REMEMBER!!!!! Multiplying and/or dividing each side of an inequality by a NEGATIVE number only produces an equivalent inequality IF the inequality sign is REVERSED!!

Solving Two-Step Inequalities… To get the ‘x’ by itself first get rid of “adding 5. ” Do the opposite. “Subtract 5. ” -3 x + 5 > -19 - 5 -5 -3 x > -24 Whatever you do to one side of the inequality you must do the other side. To get the ‘x’ by itself get rid of “multiplying by -3. ” -3 x < 8 Do the opposite. “Divide by -3 and FLIP the inequality sign” 5 6 7 8 9 10 -3 11

29 ≤ 4 x + 9 - 9 9∙ 20 ≤ 4 x 9 ∙ 4 9 4 45 ≤ x x ≥ 45 42 43 44 45 46 47 48

Solving Multi-Step Inequalities… -2(x – 6) + 7 > 35 -2(x + (-6)) + 7 > 35 -2 x + 12 + 7 > 35 “Opp-Opp” Distributive Property -2 x + 19 > 35 -19 Combine like terms “Undo” addition “Undo” multiplication, FLIP inequality symbol -11 -10 -9 -8 -7 -6 -2 x > 16 -2 -2 x < -8 -5

2 x – 1 – 4 x + 7 > 18 2 x + (-1) + (-4 x) + 7 > 18 2 x + (-4 x) + (-1) + 7 > 18 -2 x + 6 > 18 - 6 “Opp-Opp” Combine like terms “Undo” addition “Undo” multiplication and FLIP inequality symbol -9 -8 -7 -6 -5 -2 x > 12 -2 -2 x < -6 -4 -3

Solve 6 x – 7 > 2 x+17. Graph your solution. 6 x – 7 > 2 x+17 Write original inequality. 6 x > 2 x+24 Add 7 to each side. 4 x > 24 Subtract 2 x from each side. x>6 Divide each side by 4. ANSWER The solutions are all real numbers greater than 6.

Solve. 14 x + 5 < 7(2 x – 3) 14 x + 5 < 14 x – 21 5 < – 21 Write original inequality. Distributive property Subtract 14 x from each side. There are no solutions because 5 < – 21 is false. **HINT** If an inequality is equivalent to an inequality that is false, such as 5 < -21, then the solution of the inequality has NO SOLUTION.

12 x – 1 > 6(2 x – 1) 12 x – 1 > 12 x – 6 – 1>– 6 Write original inequality. Distributive property Subtract 12 x from each side. All real numbers are solutions because – 1 > – 6 is true. **HINT** If an inequality is equivalent to an inequality that is true, such as -1 > -6, then the solutions of the inequality are ALL REAL NUMBERS.

Graphs of “No Solution” and “All Real Numbers” Ø “No Solution” Ø “All Real Numbers”

You need a mean score of at least 90 points to advance to the next round of the touch-screen trivia game. What scores in the fifth game will allow you to advance?

Car Wash Use the sign shown. A gas station charges $. 10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of gasoline that you can buy if you also get a car wash and can spend at most $20? Because you are getting a car wash, you will pay $2. 09 – 2 $. 10 = $1. 99 per gallon of gasoline. Let g be the amount (in gallons) of gasoline that you buy. STEP 1 Write a verbal model. Then write an inequality. Price of gasoline (dollars/gallon) 1. 99 • Amount of gasoline (gallons) g + + Price of car wash (dollars) 8 < < – Maximum amount (dollars) 20

STEP 2 Solve the inequality. 1. 99 g + 8 ≤ 20 1. 99 g ≤ 12 g ≤ 6. 03015. . . Write inequality. Subtract 8 from each side. Divide each side by 1. 99. You can buy up to slightly more than 6 gallons of gasoline. CHECK You can use a table to check the reasonableness of your answer. The table shows that you will pay $19. 94 for exactly 6 gallons of gasoline. Because $19. 94 is less than $20, it is reasonable to conclude that you can buy slightly more than 6 gallons of gasoline. Gasoline (gal) Total amount spent (dollars) 0 8. 00 1 9. 99 2 11. 98 3 13. 97 4 15. 96 5 17. 95 6 19. 94

Homework Text p. 77, #4 -34 evens