Six friends ate in a restaurant together and split the total cost, c, equally. Each person paid less than $8. Which statements represent the scenario? Check all that apply. The total cost of the food, c, can be represented by the inequality StartFraction c Over 6 EndFraction less-than 8.

The total cost of the food could be $48
.
The total cost of the food could be $36.

When graphed, the number line would be shaded to the left of the maximum value.

The total cost of the food must be greater than $60.

100 POINTS

A, C, and D are the correct answers.

Step-by-step explanation:

A) The total cost of the food, c, can be represented by the inequality c/6 < 8

C) The total cost of the food could be $36.

D) When graphed, the number line would be shaded to the left of the maximum value.

It's A because the 6 friends SPLIT the total cost which is c, and each person paid LESS than $8 dollars, not $8 and above. So it will look like, "total cost/6 people is less than 8" aka "c/6 < 8"

It's C because if each person paid less than $8 dollars, the total is anything under 48. (6 x 8 = 48, and 6 x 6 = 36, and 6 is less than 8.)

It's D because anything LESS than the max value could be the value to c/6. So anything to the left of 8, is less than 8, and anything to the right of 8, is greater than 8, and we want what is "< 8" less than 8 so it has to be to the left.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

your answer   is c

step-by-step explanation: