Question

A number is doubled and then 3 is subtracted. This gives the same result as if the numbers were quadrupled. What is the number?

Answer 1

Let's call the number we're trying to find "x". If we double x and then subtract 3, we get the expression 2x - 3. If we quadruple x instead, we get the expression 4x. We are looking for a value of x that makes these two expressions equal, so we can set them equal to each other and solve for x:

2x - 3 = 4x

To solve this equation, we can first combine like terms on each side by adding 3 to both sides and then dividing both sides by 2:

2x - 3 + 3 = 4x + 3

2x = 4x + 3

Combining like terms on the left side gives us:

2x - 4x = 4x + 3 - 4x

0 = 3

This equation is clearly false, since no value of x can make 0 equal to 3. Therefore, there is no solution to this problem, and the original number cannot be determined.

In general, if you are trying to solve a problem involving algebraic equations and you end up with a false equation (like 0 = 3 in this case), it means that there is no solution to the problem. This can happen for a variety of reasons, but in this case it is because the original problem statement was not possible or did not make sense.

Explanation:

Answer 2

-3/2

Explanation:

Let's call the number we're trying to find "x". When we double x and then subtract 3, we get 2x-3. The statement says that this is the same as if we had quadrupled x, which would be 4x. We can set these two expressions equal to each other to create an equation:

2x - 3 = 4x

We can solve this equation by first adding 3 to both sides to get rid of the negative number:

2x - 3 + 3 = 4x + 3

This simplifies to:

2x = 4x + 3

We can now subtract 4x from both sides to get rid of the 4x term:

2x - 4x = 4x + 3 - 4x

This simplifies to:

-2x = 3

Finally, we can divide both sides by -2 to solve for x:

(-2x) / (-2) = 3 / (-2)

This simplifies to:

x = -3/2

Therefore, the number we were trying to find is -3/2.