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Simplifying sqrt(6x + 1) + sqrt(4x + 2) = sqrt(8x) + sqrt(2x + 3) Reorder the terms: qrst(1 + 6x) + sqrt(4x + 2) = sqrt(8x) + sqrt(2x + 3) (1 * qrst + 6x * qrst) + sqrt(4x + 2) = sqrt(8x) + sqrt(2x + 3) (1qrst + 6qrstx) + sqrt(4x + 2) = sqrt(8x) + sqrt(2x + 3) Reorder the terms: 1qrst + 6qrstx + qrst(2 + 4x) = sqrt(8x) + sqrt(2x + 3) 1qrst + 6qrstx + (2 * qrst + 4x * qrst) = sqrt(8x) + sqrt(2x + 3) 1qrst + 6qrstx + (2qrst + 4qrstx) = sqrt(8x) + sqrt(2x + 3) Reorder the terms: 1qrst + 2qrst + 6qrstx + 4qrstx = sqrt(8x) + sqrt(2x + 3) Combine like terms: 1qrst + 2qrst = 3qrst 3qrst + 6qrstx + 4qrstx = sqrt(8x) + sqrt(2x + 3) Combine like terms: 6qrstx + 4qrstx = 10qrstx 3qrst + 10qrstx = sqrt(8x) + sqrt(2x + 3) Remove parenthesis around (8x) 3qrst + 10qrstx = qrst * 8x + sqrt(2x + 3) Reorder the terms for easier multiplication: 3qrst + 10qrstx = 8qrst * x + sqrt(2x + 3) Multiply qrst * x 3qrst + 10qrstx = 8qrstx + sqrt(2x + 3) Reorder the terms: 3qrst + 10qrstx = 8qrstx + qrst(3 + 2x) 3qrst + 10qrstx = 8qrstx + (3 * qrst + 2x * qrst) 3qrst + 10qrstx = 8qrstx + (3qrst + 2qrstx) Reorder the terms: 3qrst + 10qrstx = 3qrst + 8qrstx + 2qrstx Combine like terms: 8qrstx + 2qrstx = 10qrstx 3qrst + 10qrstx = 3qrst + 10qrstx Add '-3qrst' to each side of the equation. 3qrst + -3qrst + 10qrstx = 3qrst + -3qrst + 10qrstx Combine like terms: 3qrst + -3qrst = 0 0 + 10qrstx = 3qrst + -3qrst + 10qrstx 10qrstx = 3qrst + -3qrst + 10qrstx Combine like terms: 3qrst + -3qrst = 0 10qrstx = 0 + 10qrstx 10qrstx = 10qrstx Add '-10qrstx' to each side of the equation. 10qrstx + -10qrstx = 10qrstx + -10qrstx Combine like terms: 10qrstx + -10qrstx = 0 0 = 10qrstx + -10qrstx Combine like terms: 10qrstx + -10qrstx = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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