Question

Drag the tiles to match each equation to its number of solutions. Each tile may be used only once. one solutionno solutioninfinitely many solutions Equation Number of Solutions –2(3x – 1) = –6x – 1 2(3x – 1) = 6x – 2 2(3x – 1) = –6x – 2

Answer 1

The first equation -2(3x - 1) = -6x - 1, has no solutions.

The second equation 2(3x – 1) = 6x – 2, has infinitely many solutions.

The third equation 2(3x – 1) = –6x – 2, has one solution.

Step-by-step explanation:

1) For the equation -2(3x - 1) = -6x - 1, we can start by simplifying both sides of the equation: -6x + 2 = -6x - 1.

Next, we can add 6x to both sides to eliminate the variable: 2 = -1.

Since this leads to a contradiction, there are no solutions for this equation.

2) For the equation 2(3x - 1) = 6x - 2, we can start by simplifying both sides of the equation: 6x - 2 = 6x - 2.

Next, we can subtract 6x from both sides to eliminate the variable: -2 = -2.

Since this equation is true for all values of x, there are infinitely many solutions.

3) For the equation 2(3x - 1) = -6x - 2, we can start by simplifying both sides of the equation: 6x - 2 = -6x - 2.

Next, we can add 6x to both sides to eliminate the variable: 12x - 2 = -2.

Then, we can add 2 to both sides: 12x = 0.

Finally, we can divide both sides by 12 to solve for x: x = 0.

Hence, there is one solution for this equation.