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Simplifying 3x + -12(3 + x) + -4t = -1(5 + -1x) + -1(7 + -1x) 3x + (3 * -12 + x * -12) + -4t = -1(5 + -1x) + -1(7 + -1x) 3x + (-36 + -12x) + -4t = -1(5 + -1x) + -1(7 + -1x) Reorder the terms: -36 + -4t + 3x + -12x = -1(5 + -1x) + -1(7 + -1x) Combine like terms: 3x + -12x = -9x -36 + -4t + -9x = -1(5 + -1x) + -1(7 + -1x) -36 + -4t + -9x = (5 * -1 + -1x * -1) + -1(7 + -1x) -36 + -4t + -9x = (-5 + 1x) + -1(7 + -1x) -36 + -4t + -9x = -5 + 1x + (7 * -1 + -1x * -1) -36 + -4t + -9x = -5 + 1x + (-7 + 1x) Reorder the terms: -36 + -4t + -9x = -5 + -7 + 1x + 1x Combine like terms: -5 + -7 = -12 -36 + -4t + -9x = -12 + 1x + 1x Combine like terms: 1x + 1x = 2x -36 + -4t + -9x = -12 + 2x Solving -36 + -4t + -9x = -12 + 2x Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '36' to each side of the equation. -36 + -4t + 36 + -9x = -12 + 36 + 2x Reorder the terms: -36 + 36 + -4t + -9x = -12 + 36 + 2x Combine like terms: -36 + 36 = 0 0 + -4t + -9x = -12 + 36 + 2x -4t + -9x = -12 + 36 + 2x Combine like terms: -12 + 36 = 24 -4t + -9x = 24 + 2x Add '9x' to each side of the equation. -4t + -9x + 9x = 24 + 2x + 9x Combine like terms: -9x + 9x = 0 -4t + 0 = 24 + 2x + 9x -4t = 24 + 2x + 9x Combine like terms: 2x + 9x = 11x -4t = 24 + 11x Divide each side by '-4'. t = -6 + -2.75x Simplifying t = -6 + -2.75x
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