Your community is having a carnival. Admission into the carnival is $6 and each game inside the carnival costs $0.75. Which of the following inequalities represents
the possible number of games g that can be played with $30?
a. 6g +0.75 s 30
b. 6g +0.75 2 30
C. 0.75g + 6 2 30
d 0.75g + 6 3 30

Hello!

The variable “g“ represents games, so the coefficient in front of it CANNOT be 6 (since $6 is the cost of the admission and you only have to pay it once).

This automatically eliminates options A and B.

We are now left with C and D.

Since the questions asks for the possible number of games played with $30, we cannot go above it. Therefore, this eliminates option C because that sign is basically telling us that the cost of the admission fee ($6) + the number of games is either greater than or equal to $30. We need it to be LESS than or EQUAL to $30.

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11