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First, let's eliminate the fractions and distribute the 1/3 to both terms within the parentheses: (1/3)*(6q - 2) = 3*(4q - 7/3q - 1/2) 2q - 2/3 = 12q - 7 - 3/2 Now, let's clear the fractions by finding the least common denominator (LCD) which is 6: 6(2q - 2/3) = 6(12q - 7 - 3/2) Now, distribute the 6 on both sides of the equation: 12q - 4 = 72q - 42 - 9 Next, let's move all the terms with the variable 'q' to the right side and constant terms to the left side: -4 + 42 + 9 = 72q - 12q Combine the like terms: 47 = 60q Now, to find the value of 'q', simply divide both sides by 60: q = 47 / 60 Since both 47 and 60 are prime, we cannot simplify this fraction further: q = 47/60
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