To solve the problem where two-thirds of a number reduced by 11 is equal to 4 more than the number, let’s define the number as x.
According to the problem, we can form the following equation:
- Two-thirds of x is represented as ⅔x.
- Reducing it by 11 gives us: ⅔x – 11.
- 4 more than x is expressed as: x + 4.
Now we can set up the equation:
⅔x - 11 = x + 4
To eliminate the fraction, we can multiply every term by 3 (the denominator) to make calculations easier:
3(⅔x) - 3(11) = 3(x + 4)
This simplifies to:
2x - 33 = 3x + 12
Now, we need to isolate x. Start by moving all x terms to one side of the equation.
2x - 3x = 12 + 33
This further simplifies to:
-x = 45
Finally, by multiplying by -1, we find:
x = -45
Thus, the number we were looking for is -45.
To verify, we can substitute -45 back into the original statement:
- Two-thirds of -45: ⅔(-45) = -30.
- Reducing by 11: -30 – 11 = -41.
- And checking 4 more than -45: -45 + 4 = -41.
Since both sides of the equation match, our solution is confirmed.