which equation has no solution?\no 4(x + 3)+2x = 6(x + 2)\no 5 + 2(3 + 2x)=x + 3(x + 1)\no 5(x + 3)+x = 4(x…

Explanation:

Step1: Simplify the first equation

[ \begin{align*} 4(x + 3)+2x&=6(x + 2)\ 4x+12 + 2x&=6x+12\ 6x+12&=6x+12 \end{align*} ] This equation has infinitely many solutions since both sides are identical.

Step2: Simplify the second equation

[ \begin{align*} 5+2(3 + 2x)&=x+3(x + 1)\ 5 + 6+4x&=x+3x+3\ 11+4x&=4x+3\ 11&\neq3 \end{align*} ] This equation has no solution as we get a false statement.

Step3: Simplify the third equation

[ \begin{align*} 5(x + 3)+x&=4(x + 3)+3\ 5x+15+x&=4x+12 + 3\ 6x+15&=4x+15\ 6x-4x&=15 - 15\ 2x&=0\ x&=0 \end{align*} ] This equation has a solution (x = 0).

Step4: Simplify the fourth equation

[ \begin{align*} 4+6(2 + x)&=2(3x + 8)\ 4+12+6x&=6x+16\ 16+6x&=6x+16 \end{align*} ] This equation has infinitely many solutions since both sides are identical.

Answer:

(5 + 2(3+2x)=x + 3(x + 1))