Final answer:
Solve the linear equation by clearing fractions, combining like terms, and then isolating x to find that x = -27/40. Ensure it is reasonable by substituting it back into the original equation.
Step-by-step explanation:
To solve for x, we start by combining like terms and simplifying the equation. The given equation is:
-(7/3)x + (1/6) = -(1/9)x + (5/3)
First, we eliminate fractions by finding a common denominator for all the terms, which in this case is 18 (the least common multiple of 3, 6, and 9).
Multiply each term by 18 to clear the fractions:
-6(7)x + 3 = -2x + 30
-42x + 3 = -2x + 30
Combine like terms and simplify:
-42x + 2x = 30 - 3
-40x = 27
Now, divide both sides by -40 to isolate x:
x = 27 / -40
Therefore, x = -27/40. This is already a reduced fraction, so it is our final answer.
Lastly, check the answer to ensure it is reasonable by substituting it back into the original equation to see if both sides balance.