1 / 16

Objectives

6.1 Solving Inequalities. Objectives. State and use symbols of inequality. Solve inequalities that involve addition and subtraction. NCSCOS. 4.01 – Use linear functions inequalities to model and solve problems. 6.1 Solving Inequalities. Rules and Properties. Statements of Inequality.

elvis-mccormick
Download Presentation

Objectives

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6.1 Solving Inequalities Objectives • State and use symbols of inequality. • Solve inequalities that involve addition and subtraction. NCSCOS • 4.01 – Use linear functions inequalities to model and solve problems.

  2. 6.1 Solving Inequalities Rules and Properties Statements of Inequality 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cless than or equal to c. a is not equal to b. a  b

  3. 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 7 < 8 If a < b, then a  c < b  c If 7 < 8 then, 7  3 < 8  3 4 < 5

  4. 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 7 > 6 If a > b, then a  c > b  c If 9 > 3 then 9  2 > 3  2 7 > 1

  5. 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. 6.1 Solving Inequalities Graph the inequalities: x 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 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 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

  7. 6.1 Solving Inequalities Solve inequalities and graph. x + 12  16 x 4 x – 8  2 6 8 10 12 14 16 18 x 10 x – 5  2 x 7 1 3 5 7 9 11 13

  8. 6.1 Solving Inequalities Solve inequalities and graph x + 4  12 x 8 4 6 8 10 12 14 x –6  2 x  8 2 4 6 8 10 12 5  x – 3 x < 8 2 4 6 8 10 12

  9. 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 x  -2 -8 -6 -4 -2 0 2

  10. 6.1 Solving Inequalities Solve the inequalities 7 3 x –> 4 4 5 x> –2–1 0 1 2 3 4 5 6 2 2 5 x +  3 9 1 x – –1 –.75 –.25 0 .25 .50 .75 9

  11. 6.1 Solving Inequalities Solve the inequalities 1) x  -19 -23 -21 -19 -17 -15 -13 -11 x  9 2) 2 3 4 5 6 7 8 9 10 12 14 3) x  17 14 16 18 20 22 24 26

  12. 6.1 Solving Inequalities Solve the inequalities 4) x  14 4 6 8 10 12 14 5) x  5 3 5 7 9 11 13 15 x  -4 6) -6 -4 -2 0 2 4 6 7) x  -3 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

  13. 6.1 Solving Inequalities 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. Let ‘d’ be the amount Michael can spend on dessert. There are two possible equations: d + $2.15 = $3.10 d + $2.15  $3.10 d + $2.15  $3.10 d  $0.95 Michael can spend no more than $0.95 on dessert.

  14. 6.1 Solving Inequalities 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. Let ‘m’ be the amount Trisha can spend on a milk shake. There are two possible equations: m + $4.69 = $6.23 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. 6.1 Solving Inequalities 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. Let ‘r’ be the amount Anne can spend on refreshments. There are two possible equations: r + $1.25 + 1.25 + 7.00 = $15.00 r + $9.50  $15.00 r + $9.50  $15.00 r  $5.50 Anne can spend no more than $5.50 on refreshments.

  16. 6.1 Solving Inequalities 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. x  376 x + 74  450 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

More Related