Let A = {6, 7, 8, 9, 10, 11, 12} and B = {8, 10, 12, 14, 16). Find the space A OR B

Explanation:

Start by writing out set A = {6,7,8,9,10,11,12}

Then introduce items from set B that aren't already in set A. So you'll introduce 14 and 16 to get the answer shown above. The answer represents all the numbers that are in set A or set B or in both sets.

A slightly similar approach is to write all of the given numbers in one big set like so

{6,7,8,9,10,11,12,    8,10,12,14,16}

then we erase the duplicates 8,10,12 to get the answer above.

When dealing with sets, we only have one unique item at a time.

We can replace the "OR" in "A OR B" with the union symbol. So we could write A U B

h/o/e/s mad

step-by-step explanation:

si si si

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.