To find the value of [tex]\( x \)[/tex] that makes the equation [tex]\((x+7)(x-4) = x^2 + 9x - 28\)[/tex] true, let's solve it step by step:
1. Expand the left-hand side:
[tex]\[
(x+7)(x-4) = x^2 - 4x + 7x - 28
\][/tex]
2. Simplify the expression on the left-hand side:
[tex]\[
x^2 - 4x + 7x - 28 = x^2 + 3x - 28
\][/tex]
3. Compare the simplified left-hand side to the right-hand side:
[tex]\[
x^2 + 3x - 28 = x^2 + 9x - 28
\][/tex]
4. Set up the equation by equating the corresponding terms:
[tex]\[
x^2 + 3x - 28 = x^2 + 9x - 28
\][/tex]
5. Since [tex]\( x^2 \)[/tex] and [tex]\(-28\)[/tex] terms cancel out, we are left with:
[tex]\[
3x = 9x
\][/tex]
6. Subtract [tex]\( 3x \)[/tex] from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
3x - 3x = 9x - 3x \implies 0 = 6x \implies x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the equation [tex]\((x+7)(x-4) = x^2 + 9x - 28\)[/tex] true is [tex]\( \boxed{0} \)[/tex]. Since [tex]\( 0 \)[/tex] is not listed among the provided options (−11, −3, 3, 11), there seems to be an error in the provided options. The correct answer is [tex]\( 0 \)[/tex].
