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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.

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

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

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

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:  

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

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

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

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

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

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

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

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.

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.

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.