Use the drop-down menus to complete each equation so the statement about its solution is true.

Part A:  For no solution ⇒ 3x + 9 + 4x + x = 8x + 0

Part B:  For one solution ⇒ 3x + 9 + 4x + x = 0 * x + 1

Part C:  For infinitely many solutions ⇒ 3x + 9 + 4x + x = 8x + 9

Step-by-step explanation:

Part A:

3x + 9 + 4x + x = 8x

8x + 9 = 8x ⇒ Subtract 6x from both sides,

9 = 0 which is absurd and hence the equation has no solution.

Part B:

3x + 9 + 4x + x = 0 * x + 1

∴ 3x + 9 + 4x + x = 1

8x + 9 = 1 ⇒ Subtract 9 from both sides.

8x = 1 - 9 = -8 ⇒ Divide both sides by 8.

x = -1      ⇒ this is the only solution.

Part C:

3x + 9 + 4x + x = 8x + 9

8x + 9 = 8x + 9

Subtract 8x from both sides,

9 = 9, both sides are balanced which means, the equation has infinitely many solutions.

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:

x

step-by-step explanation: