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?

1) Viktoriya used the distributive property incorrectly when she found the solution.
2) Viktoriya should have said that the equation has no solution.
3) Viktoriya should have continued to solve the equation to find that x = 0.
4) Viktoriya should have said that the equation has one unique solution.

Answer 1

Viktoriya erred in concluding that the equation has infinitely many solutions. The equation simplifies to the false statement -10 = -22, which indicates that the equation has no solution.

Step-by-step explanation:

The student named Viktoriya made an error when solving the equation 5 (x - 2) - 3x = 2 (x - 3) - 16. The correct process involves distributing multiplying terms correctly and keeping the equation balanced. Let's look at the steps she took:

• Apply the distributive property: 5x - 10 - 3x = 2x - 6 - 16.
• Combine like terms: 2x - 10 = 2x - 22.
• Since 2x - 2x = 0, the equation simplifies to -10 = -22, which is a false statement.

The error here lies in the conclusion drawn from the false statement. The correct conclusion from -10 = -22 is that the equation has no solution, because the statement is never true regardless of the value of x. Viktoriya incorrectly stated that the equation has infinitely many solutions, which would have been the case if the equation simplified to a true statement like 0 = 0.