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?
A. Viktoriya used the distributive property incorrectly when she found the solution.
B. Viktoriya should have said that the equation has no solution.
C. Viktoriya should have continued to solve the equation to find that x=0.
D. Viktoriya should have said that the equation has one unique solution.

Answer 1

Viktoriya's error in solving the equation is that she incorrectly used the distributive property when she found the solution. The correct steps to solve the equation are to simplify both sides of the equation, combine like terms on each side, isolate the variable, and simplify each side to determine if they are equal or not. In this case, the equation has no solution.

Step-by-step explanation:

Viktoriya's error in solving the equation is that she incorrectly used the distributive property when she found the solution. In the third step, she distributed the -10 to only one term instead of subtracting it from each term inside the parentheses. This led to an incorrect equation and an incorrect conclusion about the number of solutions.

The correct steps to solve the equation are:

1. Simplify both sides of the equation by distributing the coefficients. 5(x-2)-3x = 2(x-3)-16 becomes 5x-10-3x = 2x-6-16.
2. Combine like terms on each side of the equation. 5x-3x-10 = 2x-22 becomes 2x-10 = 2x-22.
3. Isolate the variable by subtracting 2x from both sides of the equation. 2x-2x-10 = 2x-2x-22 becomes -10 = -22.
4. Simplify each side of the equation. -10 does not equal -22.
5. Since -10 does not equal -22, the equation has no solution.