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Simplifying 4(t + -1) + -3(2t + -1) = 4 + -7(3t + 2) Reorder the terms: 4(-1 + t) + -3(2t + -1) = 4 + -7(3t + 2) (-1 * 4 + t * 4) + -3(2t + -1) = 4 + -7(3t + 2) (-4 + 4t) + -3(2t + -1) = 4 + -7(3t + 2) Reorder the terms: -4 + 4t + -3(-1 + 2t) = 4 + -7(3t + 2) -4 + 4t + (-1 * -3 + 2t * -3) = 4 + -7(3t + 2) -4 + 4t + (3 + -6t) = 4 + -7(3t + 2) Reorder the terms: -4 + 3 + 4t + -6t = 4 + -7(3t + 2) Combine like terms: -4 + 3 = -1 -1 + 4t + -6t = 4 + -7(3t + 2) Combine like terms: 4t + -6t = -2t -1 + -2t = 4 + -7(3t + 2) Reorder the terms: -1 + -2t = 4 + -7(2 + 3t) -1 + -2t = 4 + (2 * -7 + 3t * -7) -1 + -2t = 4 + (-14 + -21t) Combine like terms: 4 + -14 = -10 -1 + -2t = -10 + -21t Solving -1 + -2t = -10 + -21t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '21t' to each side of the equation. -1 + -2t + 21t = -10 + -21t + 21t Combine like terms: -2t + 21t = 19t -1 + 19t = -10 + -21t + 21t Combine like terms: -21t + 21t = 0 -1 + 19t = -10 + 0 -1 + 19t = -10 Add '1' to each side of the equation. -1 + 1 + 19t = -10 + 1 Combine like terms: -1 + 1 = 0 0 + 19t = -10 + 1 19t = -10 + 1 Combine like terms: -10 + 1 = -9 19t = -9 Divide each side by '19'. t = -0.4736842105 Simplifying t = -0.4736842105
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