4. Find the number that is 27 greater than twice the opposite of itself.

Question

UpStudy AI · Accepted Answer

Let the number be represented by $$ x $$. According to the problem, we need to find $$ x $$ such that:

$$
x = 2(-x) + 27
$$

First, simplify the right side of the equation:

$$
x = -2x + 27
$$

Next, we will add $$ 2x $$ to both sides to isolate $$ x $$:

$$
x + 2x = 27
$$

This simplifies to:

$$
3x = 27
$$

Now, divide both sides by 3 to solve for $$ x $$:

$$
x = \frac{27}{3} = 9
$$

Thus, the number is:

$$
\boxed{9}
$$

To verify, we can substitute $$ x = 9 $$ back into the original condition:

1. Calculate the opposite of $$ x $$:
   $$
   -x = -9
   $$

2. Calculate twice the opposite:
   $$
   2(-x) = 2(-9) = -18
   $$

3. Add 27 to this result:
   $$
   -18 + 27 = 9
   $$

Since this matches our original $$ x $$, the solution is confirmed. The number is indeed:

$$
\boxed{9}
$$
The number is 9.

Find the number that is 27 greater than twice the opposite of itself.