Lin is looking at the equation \(2x-32+4(3x-2462) = 14x\).

She said, “I can tell right away that there are no solutions, because on the left side, you will have \(2x+12x\) and a bunch of constants, but you have just \(14x\) on the right side.”

Do you agree with Lin? Explain your reasoning.

Han is looking at the equation \(6x-4+2(5x+2)=16x\).

He says, “I can tell right away there are no solutions, because on the left side, you will have \(6x+10x\) and a bunch of constants, but you have just \(16x\) on the right side.”

Do you agree with Han? Explain your reasoning.

Decide whether each equation is true for all, one, or no values of \(x\).

1. \(6x-4=\text-4+6x\)
2. \(4x-6=4x+3\)
3. \(\text-2x+4=\text-3x+4\)

Solve each of these equations. Explain or show your reasoning.

1. \(3(x-5) = 6\)

2. \(2\left(x - \frac{2}{3}\right) = 0\)

3. \(4x - 5 = 2 -x\)

A line is represented by the equation \(\frac{y}{x-2}=\frac{3}{11}\). For each point, determine if it is on this line.

1. \((3,13)\)
2. \((13,3)\)
3. \((35,9)\)
4. \((40, 10)\)
5. \((46, 12)\)

In the picture, quadrilateral \(A’B’C’D'\) is an image of quadrilateral \(ABCD\) after a rotation. The center of rotation is \(E\).

1. What is the length of side \(AB\)? Explain how you know.
2. What is the measure of angle \(D'\)? Explain how you know.