To determine which value of [tex]\( x \)[/tex] is a solution to the equation [tex]\((x-2)(x+5) = 18\)[/tex], we will substitute each given value for [tex]\( x \)[/tex] and check if the equation holds true.
1. Checking [tex]\( x = -10 \)[/tex]:
[tex]\[
(x-2)(x+5) = 18 \implies (-10-2)(-10+5) = (-12)(-5) = 60
\][/tex]
Since [tex]\( 60 \ne 18 \)[/tex], [tex]\( x = -10 \)[/tex] is not a solution.
2. Checking [tex]\( x = -7 \)[/tex]:
[tex]\[
(x-2)(x+5) = 18 \implies (-7-2)(-7+5) = (-9)(-2) = 18
\][/tex]
Since [tex]\( 18 = 18 \)[/tex], [tex]\( x = -7 \)[/tex] is a solution.
3. Checking [tex]\( x = -4 \)[/tex]:
[tex]\[
(x-2)(x+5) = 18 \implies (-4-2)(-4+5) = (-6)(1) = -6
\][/tex]
Since [tex]\( -6 \ne 18 \)[/tex], [tex]\( x = -4 \)[/tex] is not a solution.
4. Checking [tex]\( x = -2 \)[/tex]:
[tex]\[
(x-2)(x+5) = 18 \implies (-2-2)(-2+5) = (-4)(3) = -12
\][/tex]
Since [tex]\( -12 \ne 18 \)[/tex], [tex]\( x = -2 \)[/tex] is not a solution.
Based on these calculations, the solution to the equation [tex]\((x-2)(x+5) = 18\)[/tex] is [tex]\( x = -7 \)[/tex].
