Step 1 :The given equation is a linear equation in one variable, x. To solve for x, we need to simplify the equation and isolate x on one side of the equation.
Step 2 :First, we can combine like terms on the left side of the equation. The terms \(\frac{5}{6}x\) and \(-3x\) are like terms because they both contain the variable x.
Step 3 :Next, we can subtract \(\frac{4}{3}\) from both sides of the equation to isolate the variable term on the left side of the equation.
Step 4 :Finally, we can solve for x by dividing both sides of the equation by the coefficient of x.
Step 5 :The solution to the equation is x = -0.153846153846154. This is the value of x that makes the equation true.
Step 6 :Final Answer: The solution to the equation is \(\boxed{-0.153846153846154}\).