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Wednesday

Wednesday. Review your homework with your partner. Be ready to ask questions!!!. WEDNESDAY. Answers!!. 29/3 or 9.67 4 11. 25(7.75) + 6.25x = 250 x = 9 hours 12. 425.14 + 45x = 824.14 x = 8.87 hours. 18/3 or 6 21 3 2 All Real Numbers 16/17 or .94

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Wednesday

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  1. Wednesday • Review your homework with your partner. • Be ready to ask questions!!!

  2. WEDNESDAY Answers!! 29/3 or 9.67 4 11. 25(7.75) + 6.25x = 250 x = 9 hours 12. 425.14 + 45x = 824.14 x = 8.87 hours 18/3 or 6 21 3 2 All Real Numbers 16/17 or .94 48 -15 FIRE UP!!

  3. Tomorrow (THURSDAY) • You will need the dry erase markers tomorrow for our class work!!

  4. Unit 1 Solving Inequalities

  5. Objectives • I can solve inequalities with one variable • I can graph solutions for inequalities on a number line

  6. Solving Inequalities • Get the variable terms together on the left side of the equation • Move all the numbers to the other side of the equation. • DIVISION is the LAST step

  7. Alg-1 REVIEW

  8. Graphing the Inequalities • An open circle indicates the number is excluded from the solution • A closed circle indicates the number is included in the solution • Draw a number line with at least 3 numbers, plus the direction arrow. • Lets do some examples

  9. 1 2 3 Open Circles • Used when you have the inequality symbols (< or >). • The open circle means the number being circles is not in the solution. • x > 2 • Graph:

  10. 1 2 3 Closed Circles • Closed Circles used when the inequalities are ( or ). • Closed circles mean the number being circles is in the solution set. • x  2 • Graph:

  11. The solutions are all real numbers less than 2. An open dot is used in the graph to indicate 2 is not a solution. EXAMPLE 1 Graph simple inequalities a. Graph x < 2.

  12. The solutions are all real numbers greater than or equal to – 1. A solid dot is used in the graph to indicate – 1is a solution. EXAMPLE 1 Graph simple inequalities b. Graph x ≥ – 1.

  13. The solutions are all real numbers that are greater than – 1 and less than 2. EXAMPLE 2 Graph compound inequalities a. Graph – 1 < x < 2.

  14. The solutions are all real numbers that are less than or equal to – 2 or greater than 1. EXAMPLE 2 Graph compound inequalities b. Graph x ≤ – 2 orx > 1.

  15. Ex 1: 6x + 3 > 5x -2 • 6x + 3 > 5x –2 • x + 3 > -2 (subtracted 5x from both sides) • x > -5 (subtracted 3 from both sides)

  16. BIG DIFFERENCE If you multiply or divide each side of an inequality by a negative number then the order of the inequality must be switched.

  17. Ex 2: 3 + 2x < 3x + 9 • 3 + 2x < 3x + 9 • 3 – x < 9 (subtracted 3x from both sides) • -x < 6 ( subtracted 3 from both sides) • x > -6 (divided both sides by –1, switched the inequality sign) • x > -6

  18. ANSWER The solutions are all real numbers less than 3. The graph is shown below. EXAMPLE 4 Solve an inequality with a variable on both sides Solve 5x + 2 > 7x – 4. Then graph the solution. 5x + 2 > 7x – 4 Write original inequality. – 2x + 2 > – 4 Subtract 7xfrom each side. – 2x > – 6 Subtract 2 from each side. Divide each side by –2 and reverse the inequality. x < 3

  19. Word Problems You have $500 to replace your bathroom floor tile. The tile cost $370 and the tile saw costs $40 per hour to rent. Write and solve an inequality to find the possible numbers of hours you can rent the saw and stay under your budget.

  20. Solution: • Total money: $500 • Tile: $370 • Saw Rental: $40 per hour • Possible Inequality: • 370 + 40x ≤ 500 • x ≤ 3.25 hours

  21. Homework • WS 1-2 Inequalities • Tomorrow you will need the dry erase markers

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