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Simplifying 7(3x + 1) + 8(2x + -3) = 4(3x + -1) + -7(c + -4) Reorder the terms: 7(1 + 3x) + 8(2x + -3) = 4(3x + -1) + -7(c + -4) (1 * 7 + 3x * 7) + 8(2x + -3) = 4(3x + -1) + -7(c + -4) (7 + 21x) + 8(2x + -3) = 4(3x + -1) + -7(c + -4) Reorder the terms: 7 + 21x + 8(-3 + 2x) = 4(3x + -1) + -7(c + -4) 7 + 21x + (-3 * 8 + 2x * 8) = 4(3x + -1) + -7(c + -4) 7 + 21x + (-24 + 16x) = 4(3x + -1) + -7(c + -4) Reorder the terms: 7 + -24 + 21x + 16x = 4(3x + -1) + -7(c + -4) Combine like terms: 7 + -24 = -17 -17 + 21x + 16x = 4(3x + -1) + -7(c + -4) Combine like terms: 21x + 16x = 37x -17 + 37x = 4(3x + -1) + -7(c + -4) Reorder the terms: -17 + 37x = 4(-1 + 3x) + -7(c + -4) -17 + 37x = (-1 * 4 + 3x * 4) + -7(c + -4) -17 + 37x = (-4 + 12x) + -7(c + -4) Reorder the terms: -17 + 37x = -4 + 12x + -7(-4 + c) -17 + 37x = -4 + 12x + (-4 * -7 + c * -7) -17 + 37x = -4 + 12x + (28 + -7c) Reorder the terms: -17 + 37x = -4 + 28 + -7c + 12x Combine like terms: -4 + 28 = 24 -17 + 37x = 24 + -7c + 12x Solving -17 + 37x = 24 + -7c + 12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12x' to each side of the equation. -17 + 37x + -12x = 24 + -7c + 12x + -12x Combine like terms: 37x + -12x = 25x -17 + 25x = 24 + -7c + 12x + -12x Combine like terms: 12x + -12x = 0 -17 + 25x = 24 + -7c + 0 -17 + 25x = 24 + -7c Add '17' to each side of the equation. -17 + 17 + 25x = 24 + 17 + -7c Combine like terms: -17 + 17 = 0 0 + 25x = 24 + 17 + -7c 25x = 24 + 17 + -7c Combine like terms: 24 + 17 = 41 25x = 41 + -7c Divide each side by '25'. x = 1.64 + -0.28c Simplifying x = 1.64 + -0.28c
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