To solve for the input [tex]\( x \)[/tex] that gives an output [tex]\( y = -15 \)[/tex] in the equation [tex]\( y = 2x + 5 \)[/tex], we will follow these steps:
1. Start with the given equation:
[tex]\[
y = 2x + 5
\][/tex]
2. Substitute the given output [tex]\( y = -15 \)[/tex] into the equation:
[tex]\[
-15 = 2x + 5
\][/tex]
3. To isolate [tex]\( 2x \)[/tex], subtract 5 from both sides of the equation:
[tex]\[
-15 - 5 = 2x
\][/tex]
Simplifying this:
[tex]\[
-20 = 2x
\][/tex]
4. Now, to solve for [tex]\( x \)[/tex], divide both sides of the equation by 2:
[tex]\[
x = \frac{-20}{2}
\][/tex]
Simplifying this:
[tex]\[
x = -10
\][/tex]
Therefore, the input needed to achieve an output of [tex]\( y = -15 \)[/tex] is [tex]\(-10\)[/tex].
The correct answer is:
[tex]\[
-10
\][/tex]
