Step 1
Solve the equations to know which of them has no solution
[tex]\begin{gathered} A)x+4=2(x+4) \\ x+4=2x+8 \\ 2x-x=4-8 \\ x=-4 \\ \text{Option A has a solution} \end{gathered}[/tex][tex]\begin{gathered} B)3x+1=2x+5 \\ 3x-2x=5-1 \\ x=4 \\ \text{Option B has a solution} \end{gathered}[/tex][tex]\begin{gathered} C)\text{ 4(x-1)+2x=6x+5} \\ 4x-4+2x=6x+5 \\ 6x-6x=5+4 \\ 0=9 \\ \text{Option C has no solution} \end{gathered}[/tex][tex]\begin{gathered} D)3x+7=3x-6 \\ 3x-3x=-6-7 \\ 0=-13 \\ \text{Option D has no solution} \end{gathered}[/tex][tex]\begin{gathered} E)\text{ }4x=5x \\ 4x-5x=0 \\ -x=0 \\ x=0 \\ \text{Option E has solution} \end{gathered}[/tex][tex]\begin{gathered} F)x+1=2x \\ 2x-x=1 \\ x=1 \\ \text{Option F has solution} \end{gathered}[/tex][tex]\begin{gathered} G)x=x+7 \\ x-x=7 \\ 0=7 \\ G\text{ has no solution} \end{gathered}[/tex][tex]\begin{gathered} H)10x+1=5x-6 \\ 10x-5x=-6-1 \\ 5x=-7 \\ \frac{5x}{5}=-\frac{7}{5} \\ x=-\frac{7}{5} \\ H\text{ has a solution} \end{gathered}[/tex]
Hence C,Dand G has no solution
