Question

What number should go into the blank so that the two expressions are equivalent to each other? (Use only the digits 0 - 9 to write the number.) 10 + 5x = x + x + x + __ - 4 + x + x

Answer 1

Given:

The equation is:

`10+5x=x+x+x+\_\_\_-4+x+x`

To find:

The number for the blank so that the two expressions are equivalent to each other.

Solution:

Let n be the required number for the blank. Then,

`10+5x=x+x+x+n-4+x+x`

On combining like terms, we get

`10+5x=(x+x+x+x+x)+n-4`

`10+5x=5x+n-4`

Subtracting 5x from both sides, we get

`10=n-4`

Adding 4 on both sides, we get

`10+4=n`

`14=n`

Therefore, the required number of the blank is 14.