which equation has no solution for x?\n2(4x + 5) = 8x + 10\n3(x - 4) = 6x - 25\n4(x + 9) = 5x + 36\n6(2x…

Explanation:

Step1: Simplify equation a

$$ \begin{align*} 2(4x + 5)&=8x + 10\ 8x+10&=8x + 10\ 8x-8x&=10 - 10\ 0&=0 \end{align*} $$ This equation has infinitely many solutions.

Step2: Simplify equation b

$$ \begin{align*} 3(x - 4)&=6x-25\ 3x-12&=6x - 25\ 3x-6x&=-25 + 12\ -3x&=-13\ x&=\frac{13}{3} \end{align*} $$ This equation has one solution.

Step3: Simplify equation c

$$ \begin{align*} 4(x + 9)&=5x+36\ 4x+36&=5x + 36\ 4x-5x&=36 - 36\ -x&=0\ x&=0 \end{align*} $$ This equation has one solution.

Step4: Simplify equation d

$$ \begin{align*} 6(2x - 5)&=12x-5\ 12x-30&=12x - 5\ 12x-12x&=-5 + 30\ 0&=25 \end{align*} $$ This equation has no solution.

Answer:

D. (6(2x - 5)=12x - 5)