Certainly! Let's solve the equation step-by-step to find the value of [tex]\(x\)[/tex] that results in an output of [tex]\(-5\)[/tex].
Given the equation:
[tex]\[ y = -2x + 5 \][/tex]
We need to determine the value of [tex]\(x\)[/tex] when [tex]\(y = -5\)[/tex].
### Step-by-Step Solution:
1. Substitute the output value into the equation:
Since we want the output to be [tex]\(-5\)[/tex], we set [tex]\(y = -5\)[/tex]:
[tex]\[-5 = -2x + 5\][/tex]
2. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to perform the following algebraic steps:
- First, subtract 5 from both sides of the equation to get rid of the constant term on the right-hand side:
[tex]\[-5 - 5 = -2x + 5 - 5\][/tex]
Simplifying, we get:
[tex]\[-10 = -2x\][/tex]
- Next, divide both sides of the equation by [tex]\(-2\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[\frac{-10}{-2} = \frac{-2x}{-2}\][/tex]
Simplifying, we get:
[tex]\[x = 5\][/tex]
Therefore, the input value [tex]\(x\)[/tex] needed to achieve an output of [tex]\(-5\)[/tex] in the equation [tex]\(y = -2x + 5\)[/tex] is [tex]\(\boxed{5}\)[/tex].
