Question

Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below. 4(x – 1) – x = 3(x + 5) – 11 4x – 4 – x = 3x + 15 – 11 3x – 4 = 3x + 4 How can her partial solution be interpreted? The equation has one solution: x = 0. The equation has one solution: x = 8. The equation has no solution. The equation has infinite solutions.

Answer 1

C : The equation has no solution

Explanation:

Lily's work results in "3x – 4 = 3x + 4" which, in math, is incorrect and has no answer since no numbers can substitute for x and satisfy the equation which a correct and possible solution.

Answer 2

4(x - 1) - x = 3(x + 5) - 11

Lily's work:

1. 4(x – 1) – x = 3(x + 5) – 11
2. 4x – 4 – x = 3x + 15 – 11
3. 3x – 4 = 3x + 4

Her partial solution, 3x - 4 = 3x + 4, can be interpreted as a FALSE statement because 3x - 4 does NOT equal 3x + 4.

Since it is a false statement, the equation has no solution.