October. 27, 2014

27 Oct 2014
1 sur 20

October. 27, 2014

• 1. Today Khan Academy Notes & Practice Review for Final Exam (Next Week) Review for |Absolute Value| Test (Thursday) Usernames & Passwords for STAR math Class Work
• 2. Schedule for this week: Monday; Review for Tests, Tuesday; Meet in Room D101 Wednesday; Focus on absolute value, opposites/reciprocals, Thursday; Absolute Value Test, Friday; Begin Inequalities For the past 7 days, you have been on Khan Academy for 2403 minutes or 40.05 hours. Topics for this week (Due November 2nd):  Absolute Value Equations  Linear Equation Word Problems  Solving Rational Equations
• 4. Final Exam Review: Translate a. 8 less than the square of a number. 풙ퟐ − ퟖ b. The sum of 25 and 5 times a number ퟐퟓ + ퟓ퐲 c. Four times the difference of a number and four is eight ퟒ(풙 − ퟒ) = ퟖ The quotient of 7 and twice a number. ퟕ ퟐ풏 d. e. Write & Solve: A number is seven more than one-half of itself.
• 5. Final Exam Review: Order of Operations: Simplify 10 - 2 - 3 + 36 ÷ 4 • 9 -1 - 2 - 3 • 4 - 5 = -20 86 Simplify Expressions -5(1 – 5x) + 5( -8x -2) - 15(x +1) 2p (q + 11q - 7) 2pq + 22qp – 14p =
• 7. Addition Rule 1) When the signs are the same, ADD and keep the sign. (-2) + (-4) = 2) When the signs are different, SUBTRACT and use the sign of the larger number. (-2) + 4 = 2 + (-4) = -6 2 -2
• 8. What’s the difference between 7 - 3 and 7 + (-3) ? 7 - 3 = 4 and 7 + (-3) = 4 The only difference is that 7 - 3 is a subtraction problem and 7 + (-3) is an addition problem. “SUBTRACTING IS THE SAME AS ADDING THE OPPOSITE.”
• 9. Example #1: - 4 - (-7) = - 4 + (7) = 3 Diff. Signs --> Subtract and use larger sign. Example #2: - 3 – 7 = - 3 + (-7) -10 Same Signs --> Add and keep the sign. Which is equivalent to -12 – (-3)? 1. 12 + 3 2. -12 + 3 3. -12 - 3 4. 12 - 3
• 10. Integers Examples: Use the number line if necessary. -5 0 5 (-4) + 8 = 4 (-1) + (-3) = -4 5 + (-7) = -2 (-5) -(-3) + (-2) + (6) – (4) = -2
• 11. -1 + 3 = ? 1. -4 2. -2 3. 2 4. 4 -6 + (-3) = ? 1. -9 2. -3 3. 3 4. 9 7 – (-2) = ? 1. -9 2. -5 3. 5 4. 9
• 13. The sum of two additive inverses (or opposites) is equal to zero. Example: The additive inverse of 3 is -3 Proof: 3 + (-3) = 0 The product of two multiplicative inverses (or reciprocals) is equal to one. Ex. The multiplicative inverse of 3 is ퟏ ퟑ Proof: 3 • ퟏ ퟑ = 1
• 14. Warm-Up/Review for Final Exam Add the opposite & reciprocal of ퟐ ퟓ to the opposite & reciprocal of - ퟏ ퟒ The opposite of what number divided by ퟐ ퟑ is the opposite of eight? The reciprocal of what number a퐝퐝퐞퐝 퐭퐨 ퟕ ퟒ is two?
• 16. Absolute Value Equations: A. - 13 = - |x + 3| 1. In other words, the opposite of 13 = the opposite of |x + 3| 2. The opposite of the opposites must also be equal: 13 = |x + 3| 3. The absolute value is isolated and equal to a positive number. The two equations can now be written: 4. Solving for the positive value of the variable, the 1st equation is: |x + 3| = 13; Solving for the possibility that the variable inside the absolute value is negative, the 2nd equation is: |x + 3| = -13 10 - 16 The two possible solutions are x = and x =
• 17. Solving Absolute Value Equations Write Each Step Needed to Solve B. 5|x + 3|- 3 = 7 1. Add 3 to both sides. (When solving or ‘unwinding’ equations, we use the reverse of the order of operations, always undoing whatever is connected to the variable last) 5|x + 3| = 10 2. Divide both sides by 5: |x + 3| = 2 3. Solving for the positive is the same equation after isolating the absolute value. |x + 3| = 2 4. Write the 2nd equation. |x + 3| = - 2 5. Solve each equation separately x = -1; x = -5 6. Plug each value into original equation to confirm solution 5|-1 + 3|- 3 = 7 5|-5 + 3|- 3 = 7