Question

Given the equation 2(3x − 4) = 5x + 6, solve for the variable. Explain each step and justify your process. Charlie solved a similar equation below. Is Charlie's solution correct? Explain why or why not. 4x − 3 = 2(x − 1) 4x − 3 = 2x + 2 2x − 3 = 2 2x = 6 x =3

Answer 1

First expand the left hand side:
2(3x-4) = 6x -8. Now solve for x:

6x -5x- 8 = 5x + 6-5

x - 8 = 6

x - 8 + 8 = 6 + 8

x = 14.

No Charlie is incorrect. He incorrectly added 3 and 5. the answer to Charlie's question is x = 5/2

Answer 2

Answers are......

`x=14\\ \\ x=(1)/(2)`

Step-by-step explanation

The given equation is:
`2(3x-4)=5x+6`

First we will simplify the left side by distributing 2. So.......

`6x-8=5x+6`

Now adding 8 to both sides and subtracting 5x from both sides, we will get......

`6x-8+8-5x=5x+6+8-5x\\ \\ 6x-5x=6+8\\ \\ x=14`

So, the solution is:
`x=14`

Charlie's solution is incorrect as he made a mistake while distributing 2 on the right side.
`2(x-1)= 2x-2` The correct steps will be..........

`4x-3 = 2(x-1) \\ \\ 4x-3=2x-2\\ \\ 4x-2x=-2+3\\ \\ 2x=1\\ \\ x=(1)/(2)`

The solution of Charlie's equation will be:
`x=(1)/(2)`