What value of [tex]$g$[/tex] makes the equation true?

[tex]
(x+7)(x-4)=x^2+9x-28
[/tex]

A. [tex]$-11$[/tex]
B. [tex][tex]$-3$[/tex][/tex]
C. [tex]$3$[/tex]
D. [tex]$11$[/tex]



Answer :

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].