Sure, let's solve the problem step-by-step using algebra.
Problem Statement:
The sum of a number and 9 is multiplied by -2 and the answer is -89. Find the number.
### Step-by-Step Solution:
1. Set up the equation:
Let [tex]\( x \)[/tex] be the unknown number.
According to the problem, the sum of the number [tex]\( x \)[/tex] and 9 is multiplied by -2, and the result is -89.
So, the equation based on the problem statement will be:
[tex]\[
-2 \cdot (x + 9) = -89
\][/tex]
2. Distribute the -2 in the equation:
[tex]\[
-2x - 18 = -89
\][/tex]
Here, we distributed -2 to both [tex]\( x \)[/tex] and 9.
3. Isolate the term involving [tex]\( x \)[/tex]:
To isolate the [tex]\( x \)[/tex]-term, add 18 to both sides of the equation:
[tex]\[
-2x - 18 + 18 = -89 + 18
\][/tex]
Simplifying, we get:
[tex]\[
-2x = -71
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Now, divide both sides by -2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-71}{-2}
\][/tex]
Simplifying this fraction:
[tex]\[
x = \frac{71}{2}
\][/tex]
So, the number we were looking for is [tex]\( \frac{71}{2} \)[/tex] or 35.5.
Thus, 35.5 is the number that satisfies the given condition.
