Algebra 1 (Reiny or Kuai)

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1. Which x-values should I choose to graph these equations (y = x; y = -x + 6) so that they intersect?

2. The school band sells carnations on Valentine's Day for $2 each. They buy the carnations from a florist for $0.50 each, plus a $16 delivery charge.

a. Write a system of equations to describe the situation.

b. Graph the system. What does the solution represent?

c. Explain whether the solution shown on the graph makes sense in this situation. If not, give a reasonable solution.

3. -x/5 = 12
A: x = -60?

4. 2/5 = y/12
A: 30 = y?

5. 6(x + 2) = -2(x + 10)
A: x = -8?

6. 4 (2x + 1) > 28
A: x > 3?

7. 1/8x + 3/5 <= 3/8
A: ?

  • Algebra 1 (Reiny or Kuai) -

    1) (3,3)
    2) y = 2x
    y = .50x + 16


    3) -x/5 = 12

    X = -60
    Vertical line so slope is undefined
    4. 2/5 = y/12

    y = 12(2/5) = 24/5
    y = 24/5
    Horizontal line so slope is 0

    5) 6x + 12 = -2x -20
    8x = -32
    x = -4
    6) 8x + 4 > 28
    8x > 24
    x > 3

    7) 5x + 24 <= 15
    5x >= -9
    x <= -9/5

  • Algebra 1 (Reiny or Kuai) -

    I usually pick values of x near the origin of the x-y grid
    e.g. x = 0 , ± 1, ± 2 , ±3

    since you know it is a straight line, you really only need 2 points.
    But, I usually take a third point as a check:
    x=0 , y1 - 0 , y2 = 6
    x = 1 y1 = 1 , y2 = -1+6 = 5
    x = 4, y1 = 4, y2 = -4+6 = 2

    so I got 3 points for each of the lines
    line1 -- (0,0), (1,1) , (4,4)
    line2 -- (0,6) , (1 , 5) and (4,2)

    notice had I picked x = 3
    line1 : point (3,3)
    line 2 : point is (3,3) , well , what do you know ?!

    2 a) Don't know what you mean by the "situation"
    Was there a situation for him to buy roses for Valentines ?
    Where does the delivery charge come in ?
    In the selling of them or when they bought tem?

    #3 good
    #4 good

    #5
    6x + 12 = -2x - 20
    8x = -32
    x= -4

    #6 good

    #7
    multiply each term by 40 , the LCD, to clear the fractions
    5x + 24 ≤ 15
    5x ≤ -9
    x ≤ -9/5

  • Algebra 1 (Reiny or Kuai) -

    2. b. It represents, how many carnations needed to be carnations: 11

    c . No because the solution is not a sold to break even. Total number of carnations.

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