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Simplifying 2(t + -1) + -5(3t + -4) = 6 + -7(4t + 1) Reorder the terms: 2(-1 + t) + -5(3t + -4) = 6 + -7(4t + 1) (-1 * 2 + t * 2) + -5(3t + -4) = 6 + -7(4t + 1) (-2 + 2t) + -5(3t + -4) = 6 + -7(4t + 1) Reorder the terms: -2 + 2t + -5(-4 + 3t) = 6 + -7(4t + 1) -2 + 2t + (-4 * -5 + 3t * -5) = 6 + -7(4t + 1) -2 + 2t + (20 + -15t) = 6 + -7(4t + 1) Reorder the terms: -2 + 20 + 2t + -15t = 6 + -7(4t + 1) Combine like terms: -2 + 20 = 18 18 + 2t + -15t = 6 + -7(4t + 1) Combine like terms: 2t + -15t = -13t 18 + -13t = 6 + -7(4t + 1) Reorder the terms: 18 + -13t = 6 + -7(1 + 4t) 18 + -13t = 6 + (1 * -7 + 4t * -7) 18 + -13t = 6 + (-7 + -28t) Combine like terms: 6 + -7 = -1 18 + -13t = -1 + -28t Solving 18 + -13t = -1 + -28t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '28t' to each side of the equation. 18 + -13t + 28t = -1 + -28t + 28t Combine like terms: -13t + 28t = 15t 18 + 15t = -1 + -28t + 28t Combine like terms: -28t + 28t = 0 18 + 15t = -1 + 0 18 + 15t = -1 Add '-18' to each side of the equation. 18 + -18 + 15t = -1 + -18 Combine like terms: 18 + -18 = 0 0 + 15t = -1 + -18 15t = -1 + -18 Combine like terms: -1 + -18 = -19 15t = -19 Divide each side by '15'. t = -1.266666667 Simplifying t = -1.266666667
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