Two thirds of a number reduced by 11 is equal to 4 more than the number. Find the number.

Let’s denote the unknown number as x.

According to the problem, two thirds of the number reduced by 11 is equal to 4 more than the number. We can express this as an equation:

\( \frac{2}{3}x – 11 = x + 4 \)

Now, we’ll solve this step by step:

1. First, we can isolate the term with x on one side. We can add 11 to both sides of the equation:

\( \frac{2}{3}x = x + 4 + 11 \)

\( \frac{2}{3}x = x + 15 \)

2. Next, we want to eliminate the x on the right side. To do this, we can subtract x from both sides. We have to make x compatible with \( \frac{2}{3} \), so we write x as \( \frac{3}{3}x \):

\( \frac{2}{3}x – \frac{3}{3}x = 15 \)

\( -\frac{1}{3}x = 15 \)

3. Now, we can get rid of the negative and the fraction by multiplying both sides of the equation by -3:

\( x = -3 \times 15 \)

\( x = -45 \)

So, the number we were looking for is -45.

To verify, we can plug -45 back into the original equation:

• Two thirds of -45 is -30. Then we reduce it by 11:
  -30 – 11 = -41
• Four more than -45 is:
  -45 + 4 = -41

Since both sides are equal, our solution is confirmed. Hence, the number is -45.