To determine which of the given values for [tex]\( x \)[/tex] satisfies the equation [tex]\((x-2)(x+5) = 18\)[/tex], we need to substitute each possible solution into the equation and check if it holds true.
Let's go through each option one by one.
1. Checking [tex]\( x = -10 \)[/tex]:
[tex]\[
(x-2)(x+5) = ((-10)-2)((-10)+5)
\][/tex]
Simplify the expression:
[tex]\[
(-12)(-5) = 60
\][/tex]
The result is 60, which is not equal to 18.
2. Checking [tex]\( x = -7 \)[/tex]:
[tex]\[
(x-2)(x+5) = ((-7)-2)((-7)+5)
\][/tex]
Simplify the expression:
[tex]\[
(-9)(-2) = 18
\][/tex]
The result is 18, which means this value satisfies the equation.
3. Checking [tex]\( x = -4 \)[/tex]:
[tex]\[
(x-2)(x+5) = ((-4)-2)((-4)+5)
\][/tex]
Simplify the expression:
[tex]\[
(-6)(1) = -6
\][/tex]
The result is -6, which is not equal to 18.
4. Checking [tex]\( x = -2 \)[/tex]:
[tex]\[
(x-2)(x+5) = ((-2)-2)((-2)+5)
\][/tex]
Simplify the expression:
[tex]\[
(-4)(3) = -12
\][/tex]
The result is -12, which is not equal to 18.
From the given options, the only value that satisfies the equation [tex]\((x-2)(x+5) = 18\)[/tex] is
[tex]\[
x = -7
\][/tex]
