To determine the input [tex]\( x \)[/tex] that results in an output of [tex]\( y = -45 \)[/tex] using the equation [tex]\( y = 2x + 5 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
y = 2x + 5
\][/tex]
2. Substitute [tex]\( y = -45 \)[/tex] into the equation:
[tex]\[
-45 = 2x + 5
\][/tex]
3. To isolate [tex]\( x \)[/tex], first subtract 5 from both sides of the equation:
[tex]\[
-45 - 5 = 2x
\][/tex]
Simplify the left side:
[tex]\[
-50 = 2x
\][/tex]
4. Next, divide both sides of the equation by 2:
[tex]\[
x = \frac{-50}{2}
\][/tex]
Simplify the right side:
[tex]\[
x = -25
\][/tex]
Therefore, the input [tex]\( x \)[/tex] that results in an output of [tex]\( y = -45 \)[/tex] is [tex]\( -25 \)[/tex].
The correct answer is:
[tex]\[ -25 \][/tex]
