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?

a.The equation has one solution: x = 0.
b.The equation has one solution: x = 8.
c.The equation has no solution.
d.The equation has infinite solutions

Answer 1

c - The equation has no solution

Explanation:

4(x – 1) – x = 3(x + 5) – 11

4x – 4 – x = 3x + 15 – 11

3x – 4 = 3x + 4

Add 4 to both sides: 3x = 3x + 8

Subtract 3x from both sides: 0 = 8

The sides are not equal, therefore the equation has no solution.