Certainly! Let's solve the equation step-by-step.
Given:
The sum of a number and 9 is multiplied by -2 and the result is -8.
We need to find the unknown number. Let's denote this unknown number by [tex]\( x \)[/tex].
1. Formulate the Equation:
The problem states:
[tex]\[ -2 \times (x + 9) = -8 \][/tex]
2. Isolate the Expression Containing [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we first need to simplify the equation. Start by getting rid of the multiplication by [tex]\(-2\)[/tex]. We can do this by dividing both sides of the equation by [tex]\(-2\)[/tex]:
[tex]\[ x + 9 = \frac{-8}{-2} \][/tex]
3. Simplify the Right Side:
Divide [tex]\(-8\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[ x + 9 = 4 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
Now, we need to isolate [tex]\( x \)[/tex] by subtracting 9 from both sides of the equation:
[tex]\[ x + 9 - 9 = 4 - 9 \][/tex]
[tex]\[ x = -5 \][/tex]
So, the number that satisfies the given condition is [tex]\( \boxed{-5} \)[/tex].
