Final answer:
The solution to the linear equation 2/3x - 1/2 = 1/3 + 5/6x is x = -5, which is found by combining like terms, eliminating fractions, and isolating the variable x.
Step-by-step explanation:
The solution to the linear equation 2/3x - 1/2 = 1/3 + 5/6x can be found by following these steps:
- First, get all terms with x on one side of the equation and constants on the other. To do that, subtract 5/6x from both sides:
- (2/3x) - (5/6x) - 1/2 = 1/3
- To combine the x terms, find a common denominator, which in this case is 6. So, you get:
- (4/6x) - (5/6x) - 1/2 = 1/3
- Simplify the x terms to get:
- -1/6x - 1/2 = 1/3
- Now get rid of fractions by multiplying every term by the least common denominator, which is 6:
- -x - 3 = 2
- Add 3 to both sides to isolate the x term:
- -x = 5
- Finally, divide by -1 to solve for x:
- x = -5
Therefore, the solution to the equation is x = -5.