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To solve the equation 1/3(6q-2) = 4q-7/3q-1/2 for q, follow these steps: Step 1: Distribute the 1/3 factor. (1/3)(6q) - (1/3)(2) = 4q - 7/3q - 1/2 2q - 2/3 = 4q - 7/3q - 1/2 Step 2: Get rid of the fractions by finding the least common denominator (LCD) and multiply each term by it. The LCD for 2, 3 is 6. 6(2q - 2/3) = 6(4q - 7/3q - 1/2) Distribute the 6 to each term: 12q - 4 = 24q - 14q - 3 Step 3: Simplify the equation. 12q - 4 = 10q - 3 Step 4: Move all the q terms onto one side of the equation and the constant terms to the other side. 12q - 10q = 3 - (-4) 2q = 7 Step 5: Solve for q by dividing both sides by 2. q = 7/2 So the solution is q = 7/2.
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