The richmond family restaurant has several types of hamburgers on its menu. the more hamburgers their customers order, the more hamburger buns they will use.

h = the number of hamburgers ordered
b = the number of hamburger buns used

which of the variables is independent and which is dependent?

INDEPENDENT  variable  : h = the number of hamburgers ordered

DEPENDENT variable :   b = the number of hamburger buns used  

Step-by-step explanation:

Independent Variables: The type of variables whose change is NOT DEPENDENT on the change of other variables are known to be independent variable.

Dependent Variables: The type of variables whose change is DEPENDENT on the change of other variables are known to be independent variable.

Now here:

h = the number of hamburgers ordered

b = the number of hamburger buns used

The number of buns used depend upon the number on the buns ordered.

More buns Ordered ⇒  More buns Used

⇒  Used buns is dependent upon the order.

Hence, h = the number of hamburgers ordered  is INDEPENDENT.

b = the number of hamburger buns used    is DEPENDENT variable.

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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.