Posted by **mysterychicken** on Saturday, June 1, 2013 at 3:54pm.

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 -
**Reiny**, Sunday, June 2, 2013 at 12:06am
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 -
**Reiny**, Sunday, June 2, 2013 at 12:19am
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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