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Which is a solution to the equation?

[tex]\((x-2)(x+5) = 18\)[/tex]

A. [tex]\(x = -10\)[/tex]
B. [tex]\(x = -7\)[/tex]
C. [tex]\(x = -4\)[/tex]
D. [tex]\(x = -2\)[/tex]



Answer :

GinnyAnswer
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]

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