1. 4< 7 multiply both sides by 7, then by 6, then by 3, then by 10

2. 11> -2 add 5 to both sides, then add 3, then add (-4)

3. -4< -2 subtract 6 from both sides, then 8, and then 2

4. -8< 8 divide both sides by -4, then by -2

5. write a short explanation of the effects of the above operations. did this affect the inequality sign? was it still true? why or why not?

!

No, it didn't affect the inequality sign because we multiplied and divided by a negative number. In the 4th operation, the inequality sign changed because we divided by a negative number

Step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: