Answers are......
[tex]x=14\\ \\ x=\frac{1}{2}[/tex]
Explanation
The given equation is: [tex]2(3x-4)=5x+6[/tex]
First we will simplify the left side by distributing 2. So.......
[tex]6x-8=5x+6[/tex]
Now adding 8 to both sides and subtracting 5x from both sides, we will get......
[tex]6x-8+8-5x=5x+6+8-5x\\ \\ 6x-5x=6+8\\ \\ x=14[/tex]
So, the solution is: [tex]x=14[/tex]
Charlie's solution is incorrect as he made a mistake while distributing 2 on the right side. [tex]2(x-1)= 2x-2[/tex] The correct steps will be..........
[tex]4x-3 = 2(x-1) \\ \\ 4x-3=2x-2\\ \\ 4x-2x=-2+3\\ \\ 2x=1\\ \\ x=\frac{1}{2}[/tex]
The solution of Charlie's equation will be: [tex]x=\frac{1}{2}[/tex]
