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

2(3x-4)= 5x+ 6
6x + 8= 5x+ 6 Distribute.
6x = 5x + 14 Subtract 8 on both sides.
X= 14 Subtract 5x on both sides.


The equation with Charlie is too confusing to answer. Please be more organized next time when writing the question.

Answer 2

`x=14`

Explanation:

First it is necessary to perform the operations indicated in the parentheses.

`2(3x-4)=5x+6\\6x-8=5x+6`

Next, we will pass the terms with literal to the right side of the equation, and the constant terms to the left side. Remember that when changing side of equality, they change sign.

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

Now we will perform the indicated addition and subtraction operations

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

About charlie's equation

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

We can see that Charlie's solution is not correct. You had an error in a sign that affects the entire equation.