Question

Viktoriya solved an equation as shown below 5(x-2)-3x=2(x-3)-16 5x-10-3x=2x-6-16 2x-10=2x-22 -10=-22 She says that the equation has infinitely many solutions. Which describes Viktoriya's error?

Answer 1

Viktoriya should have said that the equation has no solution.

Answer 2

For this case we have the following equation:

`5 (x-2) -3x = 2 (x-3) -16`

The steps used by Viktoriya to solve are:

Step 1:

Distributive property:

`5x-10-3x = 2x-6-16`

Step 2:

Combine similar terms:

`2x-10 = 2x-22`

Step 3:

Simplify:

`-10 = -22`

Viktoriya's error is in the conclusion of the problem.

The equation has no solution, because:

Left side ≠ right side

Answer:

Viktoriya's error is: the equation has infinitely many solutions.