Tutors Answer Your Questions about Expressions-with-variables (FREE)
Question 329612: The following appears to prove that any two numbers are equal. Obviously it is wrong; can you spot the flaw?
Let a and b be any two different numbers. Define x as the difference between them:
x = b - a
Multiply both sides of the equation by (b-a):
x(b – a) = (b – a)(b – a)
bx – ax = b2 – 2ab + a2
Add –bx+ab-a2 to both sides and simplify:
bx – ax – bx + ab – a2 = b2 – 2ab + a2 – bx + ab – a2
bx – bx – ax + ab – a2 = –bx + b2 – 2ab + ab + a2 – a2
–ax + ab – a2 = –bx + b2 – ab
Both sides of this equation have a common factor:
a(–x + b – a) = b(–x + b – a)
Divide both sides by (-x+b-a):
a(–x + b – a) = b(–x + b – a)
–x + b – a –x + b – a
a = b
What was my mistake?
Click here to see answer by stanbon(57299)  |
Question 329612: The following appears to prove that any two numbers are equal. Obviously it is wrong; can you spot the flaw?
Let a and b be any two different numbers. Define x as the difference between them:
x = b - a
Multiply both sides of the equation by (b-a):
x(b – a) = (b – a)(b – a)
bx – ax = b2 – 2ab + a2
Add –bx+ab-a2 to both sides and simplify:
bx – ax – bx + ab – a2 = b2 – 2ab + a2 – bx + ab – a2
bx – bx – ax + ab – a2 = –bx + b2 – 2ab + ab + a2 – a2
–ax + ab – a2 = –bx + b2 – ab
Both sides of this equation have a common factor:
a(–x + b – a) = b(–x + b – a)
Divide both sides by (-x+b-a):
a(–x + b – a) = b(–x + b – a)
–x + b – a –x + b – a
a = b
What was my mistake?
Click here to see answer by galactus(183)  |
Question 329612: The following appears to prove that any two numbers are equal. Obviously it is wrong; can you spot the flaw?
Let a and b be any two different numbers. Define x as the difference between them:
x = b - a
Multiply both sides of the equation by (b-a):
x(b – a) = (b – a)(b – a)
bx – ax = b2 – 2ab + a2
Add –bx+ab-a2 to both sides and simplify:
bx – ax – bx + ab – a2 = b2 – 2ab + a2 – bx + ab – a2
bx – bx – ax + ab – a2 = –bx + b2 – 2ab + ab + a2 – a2
–ax + ab – a2 = –bx + b2 – ab
Both sides of this equation have a common factor:
a(–x + b – a) = b(–x + b – a)
Divide both sides by (-x+b-a):
a(–x + b – a) = b(–x + b – a)
–x + b – a –x + b – a
a = b
What was my mistake?
Click here to see answer by Theo(3458)  |
Question 329732: Keiko bicycles 5 km/h faster than Praedup. In the same time it takes praedup to bicycle 54 km, Keiko can bicycle 69 km. How fast does each bicyclist travel?
Praedup travels ______ km/h.
Keiko travels ________ km/h.
Click here to see answer by mananth(12270)  |
Question 329983: For the first six years, the loan value of a Corvette is determined by the formula V=-4000a + 50000, where V is the value and a is the age of the car in years. What was its original value? What is its value when it is 5 years old?
Thank you,
Shelley E.
Click here to see answer by edjones(7569)  |
Question 330699: Find the following. Assume all variables can represent any real numbers. sqrt(a+4)^2. I came up with two different answers: a+4 and then a^2+8a+16. Is either one correct? If a+4 is, does it have to be in parenthesis or |a+4|? Please advise. Thank you.
Click here to see answer by Fombitz(13828)  |
Question 330937: Judy and Mary started walking toward each other from two different locations. They started at the same time. Judsy walks 2 miles per hour and Mary walks 2.5 miles per hour. By the time Judy reached mid point, they were 3 miles apart. How far apart were they when they started?
Click here to see answer by stanbon(57299) |
Question 330939: Imagine a driver with straight parallel sides and no current. Boat a departs side A at the same time as boat b departs side B, both perpendicular to the riverbank, and both at constant (but possibly different) speeds. They pass each other 800 yards from A, proceed to the opposite shore, turn around, and pass again 400 yards from B. How wide is the river?
Click here to see answer by galactus(183) |
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