Question

What is the solution to the linear equation?

x – StartFraction 2 Over 3 EndFraction x minus StartFraction one-half EndFraction equals StartFraction 1 Over 3 EndFraction plus StartFraction 5 Over 6 EndFraction x. = + x

x = –5
x = –negative StartFraction 1 Over 6 EndFraction
x = StartFraction 1 Over 6 EndFraction
x = 5

Answer 1

The text is ambiguous about parentheses. For the three common interpretations:

1) If the equation is x − (2/3)x − 1/2 = 1/3 + (5/6)x:
- Combine left: (1/3)x − 1/2 = 1/3 + (5/6)x
- Bring x-terms to one side: −(1/2)x = 5/6
- So x = −10/6 = −5/3.

2) If the equation is x − (2/3)(x − 1/2) = 1/3 + (5/6)x:
- Expand left: x − (2/3)x + 1/3 = 1/3 + (5/6)x
- Simplify: (1/3)x + 1/3 = 1/3 + (5/6)x → (1/3)x = (5/6)x → x = 0.

3) If the equation is x − (2/3)x − (1/2)x = 1/3 + (5/6)x:
- Left: (−1/6)x = 1/3 + (5/6)x → −x = 1/3 → x = −1/3.

Which of these matches the way the problem was meant? (With the most straightforward reading 1) the solution is x = −5/3, which is not among the four choices you listed.)