Final answer:
To solve (5x+3)/7 = x/2, multiply by 14, simplify, and solve for x, yielding the solution x = -2.
Step-by-step explanation:
To solve the equation (5x+3)/7 = x/2 for x, first, clear the denominators by multiplying each side of the equation by 14 (the least common multiple of 7 and 2). This yields 2(5x+3) = 7x, which simplifies to 10x + 6 = 7x. Subtracting 7x from both sides gives 3x + 6, and after subtracting 6 from both sides, you get 3x = -6. Dividing both sides by 3 yields the solution, x = -2.