A number is multiplied by 4 and 6 is subtracted from it . The result is the same as when the number is increased by 15. Find the number

4x-6 = x+15

Let's solve this algebraically step by step:

Let's assume the number we are looking for is "x".

According to the problem, "A number is multiplied by 4 and 6 is subtracted from it." We can write this as:
4x - 6

The problem also states that "the result is the same as when the number is increased by 15." This can be expressed as:
x + 15

Now we can set up an equation using our expressions:

4x - 6 = x + 15

To solve for x, we need to isolate the variable on one side of the equation.

Let's first get rid of x on the right side of the equation by subtracting x from both sides:

4x - x - 6 = x - x + 15

This simplifies to:
3x - 6 = 15

Next, let's isolate the constant term by adding 6 to both sides:

3x - 6 + 6 = 15 + 6

This simplifies to:
3x = 21

Finally, we can solve for x by dividing both sides by 3:

3x/3 = 21/3

This gives us:
x = 7

Therefore, the number we are looking for is 7.