9) Solve the equation for x: (3x + y)/z = 2

10) ...

**8) Absolute value is the distance from zero on a number line (and has no reference to which direction left/right from zero), so this means the value is always positive:*** abs(2) = 2**abs(-2) = 2***9) Solve the equation for x**

(3x + y)/z = 2

*multiply both sides by z

(3x + y) = 2z

*subtract y from both sides

3x = 2z - y

*divide both sides by 3

x = (2z - y)/3**10) Which point is a solution to the equation 6x - 5y = 4? Justify your choice****A. (1, 2)****B. (1,2)****C. (-1,2)****D. (-1, 2)**

*plug (x, y) coordinates into equation and see if the result is a valid equation:

*start with A. (1, 2):

6(1) - 5(2) = 4

6 - 10 = 4

-4 = 4 [NO GOOD]

*now try B. (1,2):

6(1) - 5(-2) = 4

6 - (-10) = 4

6 + 10 = 4

16 = 4 [NO GOOD]

*now try C. (-1,2):

6(-1) - 5(-2) = 4

-6 - (-10) = 4

-6 + 10 = 4* 4 = 4 [OK]*

*just for fun let’s also verify D. (-1, 2) is not the solution, since we found that C. was:

6(-1) - 5(2) = 4

-6 - 10 = 4

-16 = 4 [NO GOOD]*The answer is C. (-1,2) (and the justification is that we solved for it to be true)***11) Domain is all values ’x’ (i. e. input)**** Range is all values ’y’ (i. e. output)**

a. ) y = 2x + 1 is a line with a slope of 2:1 (vert: horiz) and a y-intercept of y = 1, but because it is a line, it extends from -infinty to +infinity for both ’x’ and ’y’, so. *Domain = (-infinity ≤ x ≤ +infinity)**Range = (-infinity ≤ y ≤ +infinity)*

b. ) This table on shows discrete values of input/output, so the domain/range is also discrete. *Domain = (3, 7, 11)**Range = (-1,3,5)*

c. ) Just from visual confirmation of the plot’s extents. *Domain = (-5 ≤ x ≤ 5)**Range = (-1 ≤ y ≤ 1)*

d. ) Again using visual confirmation of the plot’s extents. *Domain = (-2 ≤ x ≤ 2) *note extents are limited by vertical asymptote**Range = (-infinity ≤ y ≤ +infinity)*

12) There are ** 2 lines of symmetry** (they are the vertical line drawn at x = 0, and the horizontal line drawn at y = 0 that bisect the ellipse)