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Simplifying sqrt(4x + 1) + sqrt(3x + -2) = sqrt(2x + -3) + sqrt(5x + 6) Reorder the terms: qrst(1 + 4x) + sqrt(3x + -2) = sqrt(2x + -3) + sqrt(5x + 6) (1 * qrst + 4x * qrst) + sqrt(3x + -2) = sqrt(2x + -3) + sqrt(5x + 6) (1qrst + 4qrstx) + sqrt(3x + -2) = sqrt(2x + -3) + sqrt(5x + 6) Reorder the terms: 1qrst + 4qrstx + qrst(-2 + 3x) = sqrt(2x + -3) + sqrt(5x + 6) 1qrst + 4qrstx + (-2 * qrst + 3x * qrst) = sqrt(2x + -3) + sqrt(5x + 6) 1qrst + 4qrstx + (-2qrst + 3qrstx) = sqrt(2x + -3) + sqrt(5x + 6) Reorder the terms: 1qrst + -2qrst + 4qrstx + 3qrstx = sqrt(2x + -3) + sqrt(5x + 6) Combine like terms: 1qrst + -2qrst = -1qrst -1qrst + 4qrstx + 3qrstx = sqrt(2x + -3) + sqrt(5x + 6) Combine like terms: 4qrstx + 3qrstx = 7qrstx -1qrst + 7qrstx = sqrt(2x + -3) + sqrt(5x + 6) Reorder the terms: -1qrst + 7qrstx = qrst(-3 + 2x) + sqrt(5x + 6) -1qrst + 7qrstx = (-3 * qrst + 2x * qrst) + sqrt(5x + 6) -1qrst + 7qrstx = (-3qrst + 2qrstx) + sqrt(5x + 6) Reorder the terms: -1qrst + 7qrstx = -3qrst + 2qrstx + qrst(6 + 5x) -1qrst + 7qrstx = -3qrst + 2qrstx + (6 * qrst + 5x * qrst) -1qrst + 7qrstx = -3qrst + 2qrstx + (6qrst + 5qrstx) Reorder the terms: -1qrst + 7qrstx = -3qrst + 6qrst + 2qrstx + 5qrstx Combine like terms: -3qrst + 6qrst = 3qrst -1qrst + 7qrstx = 3qrst + 2qrstx + 5qrstx Combine like terms: 2qrstx + 5qrstx = 7qrstx -1qrst + 7qrstx = 3qrst + 7qrstx Add '-7qrstx' to each side of the equation. -1qrst + 7qrstx + -7qrstx = 3qrst + 7qrstx + -7qrstx Combine like terms: 7qrstx + -7qrstx = 0 -1qrst + 0 = 3qrst + 7qrstx + -7qrstx -1qrst = 3qrst + 7qrstx + -7qrstx Combine like terms: 7qrstx + -7qrstx = 0 -1qrst = 3qrst + 0 -1qrst = 3qrst Solving -1qrst = 3qrst Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3qrst' to each side of the equation. -1qrst + -3qrst = 3qrst + -3qrst Combine like terms: -1qrst + -3qrst = -4qrst -4qrst = 3qrst + -3qrst Combine like terms: 3qrst + -3qrst = 0 -4qrst = 0 Divide each side by '-4'. qrst = 0 Simplifying qrst = 0 The solution to this equation could not be determined.
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