Define a#b=ab-a-b+1 for all real numbers a and b. x # 7 = 42. What is the value of x?
We are told : a#b=ab-a-b+1
so x#7 = 7x - x - 7 +1 = 42
6x = 48
x = 8
Well, it seems like you stumbled upon a bit of mathematical clownery! Let me show you the magic, or should I say, mathematic trickery.
We have the equation x # 7 = 42. Substituting the given definition of # into the equation, we get:
x(7) - x - 7 + 1 = 42
Simplifying this equation, we have:
7x - x - 6 = 42
Combining like terms:
6x - 6 = 42
Adding 6 to both sides:
6x = 48
Dividing both sides by 6, we find:
x = 8
So, my mathematical friend, the value of x when x # 7 equals 42 is 8. But remember, this is all just clowning around, so don't take it too seriously!
To find the value of x, we need to substitute the given value of # into the equation x # 7 = 42.
Using the definition of #, we plug in the values:
x # 7 = 42
x(7) - x - 7 + 1 = 42
Simplifying the equation:
7x - x - 6 = 42
(7 - 1)x = 48
6x = 48
Dividing both sides of the equation by 6:
6x/6 = 48/6
x = 8
Therefore, the value of x is 8.
To find the value of x in the equation x # 7 = 42 using the given definition of the operator "#", we can substitute the value of "7" for b.
Let's plug in the values into the equation:
x # 7 = 42
Substitute b = 7 into the definition of "#":
x # 7 = (x * 7) - x - 7 + 1
Simplify the expression:
x * 7 - x - 7 + 1 = 42
Now, let's combine like terms:
6x - 6 = 42
To isolate x, let's add 6 to both sides of the equation:
6x = 42 + 6
Simplify:
6x = 48
Finally, divide both sides of the equation by 6 to solve for x:
x = 48 / 6
x = 8
Therefore, the value of x is 8.