SAT math

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1. x>15-2x / -3 Solve the linear inequality. Write the solution in set builder notation.
So, -3x>15-2x, x<-15..?
And how do I write it in set builder notation?

2. y+x=9 and 3y=2x + 8. How do I solve this system of equations?

3. Find the maximum y- value of the following quadratic function: f(x)= -2x^2 + 7x + 1

4. Solve the following equation: 4x/3 + 1/2 = 5y/6
I'm not even sure what this question is asking...

5. Find the solution set to the equation below: 2*absolute value of x-100 = 50 +absolute value of x-100.
x = 150?

  • SAT math -

    x > (15-2x)/-3
    looks like you multiplied both sides by -3, but did not reverse the inequality sign.
    should have been:
    -3x < 15 - 2x
    -x < 15
    x> -15

    {x | x > -15 }

    2. I would use substitution.
    from the first: y =9-x
    sub into the 2nd:
    3(9-x) = 2x+8
    27 - 3x = 2x + 8
    -5x = -19
    x = 19/5 = 3.8
    y = 9-3.8 = 5.2

  • SAT math -

    3. Find the maximum y- value of the following quadratic function: f(x)= -2x^2 + 7x + 1

    The maximum value of the y value is obtained from the vertex
    the x of the vertex is -b/(2a) = -7/-4 = 7/4
    y = -2(49/16) + 7(7/4) + 1 = 57/8


    4.
    4x/3 + 1/2 = 5y/6
    multiply each term by 6
    8x + 3 = 5y
    8x + 5y + 3 = 0
    ----> the equation of a straight line, with slope of -5/3
    "solve" is not the correct instruction for this equation.

    5.

    2|x-100| = 50 + |x-100|

    2(x-100) = 50 + |x-100| OR -2(x-100) = 50 + |x-100|

    case1 :
    2(x-100) = 50 + |x-100|
    2x - 200 = 50 + |x-100|
    2x - 250 = |x-100|

    x-100 = 2x-250 OR x-100 = -2x + 250
    -x = -150 OR 3x = 350
    x = 150 OR x = 350/3

    case2:
    -2(x-100) = 50 + |x-100|
    -2x + 100-50 = |x-100|
    -2x + 50 = |x-100|
    x-100 = -2x + 50 OR x-100 = 2x - 50
    3x = 150 OR -x = 50
    x = 50 or x = -50

    x = ±50 , 150 , 350/3

    check my arithmetic on the last one

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