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

The 3rd option i.e. 'the equation has no solution' is the correct option.

Explanation:

Given the given function

4(x – 1) – x = 3(x + 5) – 11

Lily's work is shown below

4(x – 1) – x = 3(x + 5) – 11

4x – 4 – x = 3x + 15 – 11

3x – 4 = 3x + 4

It is clear that the Left-hand side of the equation is not equal to the right-hand side of the equation as 3x – 4 can not be equal to 3x + 4.

i.e.

3x – 4 ≠ 3x + 4

3x - 3x -4 ≠ 4

-4 ≠ 4

L.H.S ≠ R.H.S

Therefore, the equation has no solution.

Hence, the 3rd option i.e. 'the equation has no solution' is the correct option.