At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply.

It is given that the cup is filled with 4 oz. of yogurt before any toppings are added. So, the initial weight of the cup must greater than or equal to 4.

[tex]x\geq 4[/tex] ........(1)

After that toppings are added, they are allowed up to a total weight of 6 oz.

So, the weight of the cup cannot be more that 6

[tex]x\leq 6[/tex] ........(2)

On combining (1) and (2). We get

[tex]4\leq x\leq 6[/tex]

The acceptable weights for the frozen yogurt is represented by the inequality [tex]4\leq x\leq 6[/tex].

It means option C is correct and options A, B and D are incorrect.

In option E,

[tex]|x-5|\leq 1[/tex]

[tex]-1leq x-5\leq 1[/tex]

Add 5 on each sides.

[tex]4 leq x\leq 6[/tex]

Option E is correct.

In option F,

[tex]|x-2|\leq 6[/tex]

[tex]-6 leq x-2\leq 6[/tex]

Add 2 on each sides.

[tex]-4 leq x\leq 8[/tex]

Option F is incorrect.

Therefore, the correct options are C and E.