1. Lesson 6.1 & 6.2

2. Learning Goal for Focus 2 (HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3): The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step. 43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: - Make connection with other concepts in math - Make connection with other content areas. The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step. - rearrange formulas to highlight a quantity of interest. -Graph created equations on a coordinate graph. The student will be able to solve linear equations and inequalities in one variable and explain the logic in each step. -Use equations and inequalities in one variable to solve problems. With help from the teacher, the student has partial success with solving linear equations and inequalities in one variable. Even with help, the student has no success with solving linear equations and inequalities in one variable.

3. To graph Inequalities: Use an open circle for then shade the line in for which direction it will go. Use a closed circle for ≤ or ≥ then shade the line in for which direction it will go. Example: x< 4 123456

4. write and graph each of the following inequalities. The summer temperature T, in Phoenix is greater than or equal to 80 degrees. The average snow fall is less than one inch. The class average is greater than or equal to 85%. T ≥ 80 degrees 777879808182 S < 1 inch -2 -1 0 1 2 3 4 A ≥ 85%828384858687

5. Tips to Solving Linear Inequalities: Solve just like an equation Get the variable alone on one side Remember if you multiply or divide by a negative number to get the variable alone, reverse (change) the inequality symbol!

6. Example: 2x + 3 > 4 As an equation 2x + 3 = 4 -3 -3 2x = 1 2 2 x = As an inequality 2x + 3 > 4 - 3 -3 2x > 1 2 2 x > Notice the x value is the same. Now graph your answer. 1023

7. Practice: solve and graph -5x + 8 ≤ 43 -5x ≤ 35 x ≥ -7 -10 -9 -8 -7 -6 -5 -4 -3 REMEMBER: When you multiply or divide by a negative number you MUST change the direction of the inequality.

8. Practice: solve and graph x + 3 ≤ 2(x-4) x + 3 ≤ 2x – 8 -x -x 3 ≤ x – 8 +8 +8 11 ≤ x which means x ≥ 11 8 9 10 11 12 13 14 15

9. In Owego, NY, the temperature in January may not exceed 0 degrees C. Write an inequality that describes temperature T for the month and graph it. T ≤ 0 -2 -1 0 1 2 3 4

10. You have $32.14 in your pocket that you want to spend on a new pair of shoes. If sales tax is 6%, what’s the most your shoes can cost before tax? Label what you know: You have = $32.14 Sales tax =.06 “x” cost of shoes Write an inequality. x + x(.06) ≤ 32.14 Solve 1.06x ≤ 32.14 x ≤ 30.32 Answer the question: The shoes can cost up to $30.32 and you would have enough money to pay for them. Problem Solving With Inequalities

11. You need some new CD’s to copy your photos on to send to your grandma in St. Louis. You found a great deal where you can get CD’s for $3.00 each plus a flat shipping fee of $2.00. If you have $25.00 to spend, how many CD’s can you order? The last problem to solve together: Label what you know: CDs= $3 Shipping = $2 You have = $25 “x” number of CDs Write an inequality. 3x + 2 ≤ 25 Solve 3x ≤ 23 x ≤ 7 2 / 3 Answer the question: You can order up to 7 CDs and have enough money to pay for them.