Final answer:
To solve the given equation, find a common denominator, eliminate the fractions, combine like terms, and isolate x to find that x = 10/39.
Step-by-step explanation:
To solve the equation 2/3 - 4x + 7/2 = 9x + 5/6, we need to combine like terms and isolate the variable, x. Let's first find a common denominator for the fractions involved in the equation to make it easier to combine them. We can use 6 as a common denominator since it is the least common multiple of 2, 3, and 6.
Multiplying each term by 6 to eliminate the denominators, we get:
4 - 24x + 21 = 54x + 5.
Combining like terms, we have:
25 - 24x = 54x + 5,
Now, add 24x to both sides to get all the x terms on one side:
25 = 78x + 5.
Subtract 5 from both sides:
20 = 78x,
Now, divide both sides by 78 to solve for x:
x = 20/78. Simplifying the fraction, we get x = 10/39.