Which of the following equations has no solution? $\newline$ $x+3x+6=6+4x$ $\newline$ $3x-2=2-3x$ $\newline$ $2x+7x-5=9x+5$ $\newline$ $4x-5x+3=-5x+4x-3$

Full solution

Q. Which of the following equations has no solution?

\newline

x+3x+6=6+4x

\newline

3x-2=2-3x

\newline

2x+7x-5=9x+5

\newline

4x-5x+3=-5x+4x-3

Simplify Equations: Step Title: Simplify and Compare Each Equation $\newline$ Concise Step Description: Simplify each equation to see if they result in contradictions or identities. $\newline$ Step Calculation: $\newline$ $1$ . $x + 3x + 6 = 6 + 4x$ $\newline$ $4x + 6 = 6 + 4x$ $\newline$ $6 = 6$ (Identity, not no solution) $\newline$ $2$ . $3x - 2 = 2 - 3x$ $\newline$ $3x + 3x = 2 + 2$ $\newline$ $6x = 4$ $\newline$ $x = \frac{4}{6}$ $\newline$ $x = \frac{2}{3}$ (Solution exists) $\newline$ $3$ . $2x + 7x - 5 = 9x + 5$ $\newline$ $9x - 5 = 9x + 5$ $\newline$ $4x + 6 = 6 + 4x$ $0$ (Contradiction, no solution) $\newline$ $4$ . $4x + 6 = 6 + 4x$ $1$ $\newline$ $4x + 6 = 6 + 4x$ $2$ $\newline$ $4x + 6 = 6 + 4x$ $3$ (Contradiction, no solution)