1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) Objectives State and use symbols of inequality. Solve inequalities that involve addition and subtraction. 6.1 Solving Inequalities NCSCOS 4.01 – Use linear functions inequalities to model and solve problems.

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) Rules and Properties 6.1 Solving Inequalities a is less than b. a < b a is greater than b. a > b a is less than or equal to b. a  b a is greater than or equal to b. a  b a is greater than b and less than c. b < a < c a is greater than or equal to b and b  a  c less than or equal to c. a is not equal to b. a  b Statements of Inequality

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Inequality Addition and Subtraction Let a, b, and c be real numbers. If a < b, then a + c < b + c If 4 < 5 then, 4 + 3 < 5 + 3 If a < b, then a  c < b  c If 7 < 8 then, 7  3 < 8  3 7 < 8 4 < 5

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Inequality Addition and Subtraction Let a, b, and c be real numbers. If a > b, then a + c > b + c If 6 > 5 then 6 + 1 > 5 + 1 If a > b, then a  c > b  c If 9 > 3 then 9  2 > 3  2 7 > 6 7 > 1

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Graphing number lines: Greater than or equal to: - use a closed circle on a number line: Less than or equal to: - use a closed circle on a number line:   Greater than: - use an open circle on a number line: Less than: - use an open circle on a number line:  

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Graph the inequalities: x  3 x  0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 x  5 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 x  -4

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Solve inequalities and graph. x + 12  16 x  4 x – 8  2 x  10 x – 5  2 x  7 6 8 10 12 14 16 18 1 3 5 7 9 11 13

8. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Solve inequalities and graph x + 4  12 x  8 x – 6  2 x  8 4 6 8 10 12 14 2 4 6 8 10 12 5  x – 3 2 4 6 8 10 12 x < 8

9. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Solve the inequalities 18 + x  –6 x  –24 -30 -28 -26 -24 -22 -20 -18 7 + x  –6 x  –13 -23 -21 -19 -17 -15 -13 -11 x + 4  2 -8 -6 -4 -2 0 2 x  -2

10. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Solve the inequalities x – > x > 7 4 3 4 5 2 –2 –1 0 1 2 3 4 5 6 x +  x  – 2 3 5 9 1 9 –1 –.75 –.25 0.25.50.75

11. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Solve the inequalities -23 -21 -19 -17 -15 -13 -11 1) 2 3 4 5 6 7 8 9 10 12 14 2) 14 16 18 20 22 24 26 3) x  -19 x  9 x  17

12. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 6.1 Solving Inequalities Solve the inequalities 4) 3 5 7 9 11 13 15 5) 4 6 8 10 12 14 x  14 x  5 6) -6 -4 -2 0 2 4 6 x  -4 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 7) x  -3

13. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) Michael can spend at most $3.10 for lunch. He buys a hamburger and a drink for $2.15. Write an inequality that models how much Michael can spend on dessert and stay within his spending limits. d + $2.15 = $3.10 Let ‘d’ be the amount Michael can spend on dessert. 6.1 Solving Inequalities There are two possible equations: d + $2.15  $3.10 d + $2.15  $3.10 d  $0.95 Michael can spend no more than $0.95 on dessert.

14. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) Trisha has only $6.23 to spend for lunch. She buys a cheeseburger, fries, and a drink for $4.69. Write an inequality that models how much Trisha can spend on a milk shake and stay within her spending limits. m + $4.69 = $6.23 Let ‘m’ be the amount Trisha can spend on a milk shake. 6.1 Solving Inequalities There are two possible equations: m + $4.69  $6.23 m + $4.69  $6.23 m  $1.54 Trisha can spend no more than $1.54 to buy a milk shake.

15. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) Anne can spend at most $15.00 when she goes to see a movie. She has to spend $1.25 each way for a subway ride, and the movie ticket is $7.00. Write an inequality that models how much Anne can spend on refreshments and stay within her spending limits. r + $1.25 + 1.25 + 7.00 = $15.00 Let ‘r’ be the amount Anne can spend on refreshments. 6.1 Solving Inequalities There are two possible equations: r + $9.50  $15.00 r + $9.50  $15.00 r  $5.50 Anne can spend no more than $5.50 on refreshments.

16. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) A school auditorium can seat 450 people for graduation. The graduates will use 74 seats. Write and solve an inequality to describe the number of additional people who can be seated in the auditorium. 6.1 Solving Inequalities x + 74  450 x  376 Write and solve an inequality to describe the number of additional seats in an auditorium if the school auditorium can seat 450 people for graduation. Graduates will use 74 seats and their personal family and friends will use 370 seats. x + 444  450 x  6