Question

@Jim766
I would like to know the correct answer to this problem I got wrong
@phi

Answer 1

f(x) = x - 3
g(x) = -0.5 x

(f-g)(x) means figure out f(x) - g(x) = x -3 - (-0.5x)
we get
x -3 + 0.5x
combine the "like terms" x+0.5x to get 1.5x

and
1.5x - 3

Answer 2

now we need to find
1.5x - 3 < 0
in other words, find the x values where the expression 1.5x-3 is negative

if we write 1.5 as the fraction 3/2 we have
\[ \frac{3}{2} x - 3 < 0 \]
add 3 to both sides
\[ \frac{3}{2} x - 3+3 < 0 +3\\ \frac{3}{2} x < 3\]
now multiply both sides by ⅔ and simplify
\[ x < 3\cdot \frac{2}{3} \\ x < 2 \]

Answer 3

Therefore, the answer is C.

Answer 4

x < 2
is short for
"all numbers less than 2 (but not equal to 2)"

Answer 5

(a,b) means all numbers bigger than a and less than b

example: (0,3) means all numbers bigger than 0 but less than 3

Answer 6

you want the choice the means x < 2
i.e. any number smaller than 2

(0,3) means a number bigger than 0 and less than 2. In other words, numbers like -1 are not part of (0,3). But -1 is less than 2, and is part of the answer. (0,3) is not the correct choice.

Answer 7

B must be the correct choice, greater than negative infinity and less than 2 :)

Answer 8

yes

Answer 9

^thank you.

Answer 10

yw