which of these equations has no solution?\n3(2x + 7) = 6(x + 4) - 3\n3(6x - 5) = 3(6x - 5) + x\n8(x - 3) +…

Explanation:

Step1: Simplify the first equation

$$ \begin{align*} 3(2x + 7)&=6(x + 4)-3\ 6x+21&=6x + 24-3\ 6x+21&=6x+21 \end{align*} $$ This equation has infinitely many solutions.

Step2: Simplify the second equation

$$ \begin{align*} 3(6x - 5)&=3(6x - 5)+x\ 18x-15&=18x-15 + x\ 18x-15&=19x-15\ 18x-19x&=-15 + 15\ -x&=0\ x&=0 \end{align*} $$ This equation has one solution.

Step3: Simplify the third equation

$$ \begin{align*} 8(x - 3)+14&=2(4x + 5)\ 8x-24 + 14&=8x+10\ 8x-10&=8x+10\ 8x-8x&=10 + 10\ 0&=20 \end{align*} $$ This equation has no solution.

Step4: Simplify the fourth equation

$$ \begin{align*} 13x-7&=12(x - 1)+x+5\ 13x-7&=12x-12+x + 5\ 13x-7&=13x-7 \end{align*} $$ This equation has infinitely many solutions.

Answer:

The equation (8(x - 3)+14 = 2(4x + 5)) has no solution.