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Simplifying 7(4x + -2) + 3(17 + -4c) = 3(5x + 2) + -3 Reorder the terms: 7(-2 + 4x) + 3(17 + -4c) = 3(5x + 2) + -3 (-2 * 7 + 4x * 7) + 3(17 + -4c) = 3(5x + 2) + -3 (-14 + 28x) + 3(17 + -4c) = 3(5x + 2) + -3 -14 + 28x + (17 * 3 + -4c * 3) = 3(5x + 2) + -3 -14 + 28x + (51 + -12c) = 3(5x + 2) + -3 Reorder the terms: -14 + 51 + -12c + 28x = 3(5x + 2) + -3 Combine like terms: -14 + 51 = 37 37 + -12c + 28x = 3(5x + 2) + -3 Reorder the terms: 37 + -12c + 28x = 3(2 + 5x) + -3 37 + -12c + 28x = (2 * 3 + 5x * 3) + -3 37 + -12c + 28x = (6 + 15x) + -3 Reorder the terms: 37 + -12c + 28x = 6 + -3 + 15x Combine like terms: 6 + -3 = 3 37 + -12c + 28x = 3 + 15x Solving 37 + -12c + 28x = 3 + 15x Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -12c + -37 + 28x = 3 + -37 + 15x Reorder the terms: 37 + -37 + -12c + 28x = 3 + -37 + 15x Combine like terms: 37 + -37 = 0 0 + -12c + 28x = 3 + -37 + 15x -12c + 28x = 3 + -37 + 15x Combine like terms: 3 + -37 = -34 -12c + 28x = -34 + 15x Add '-28x' to each side of the equation. -12c + 28x + -28x = -34 + 15x + -28x Combine like terms: 28x + -28x = 0 -12c + 0 = -34 + 15x + -28x -12c = -34 + 15x + -28x Combine like terms: 15x + -28x = -13x -12c = -34 + -13x Divide each side by '-12'. c = 2.833333333 + 1.083333333x Simplifying c = 2.833333333 + 1.083333333x
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