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Simplifying 6(3t + -4) + 10 = 5(t + -2) + -1(3t + -4) Reorder the terms: 6(-4 + 3t) + 10 = 5(t + -2) + -1(3t + -4) (-4 * 6 + 3t * 6) + 10 = 5(t + -2) + -1(3t + -4) (-24 + 18t) + 10 = 5(t + -2) + -1(3t + -4) Reorder the terms: -24 + 10 + 18t = 5(t + -2) + -1(3t + -4) Combine like terms: -24 + 10 = -14 -14 + 18t = 5(t + -2) + -1(3t + -4) Reorder the terms: -14 + 18t = 5(-2 + t) + -1(3t + -4) -14 + 18t = (-2 * 5 + t * 5) + -1(3t + -4) -14 + 18t = (-10 + 5t) + -1(3t + -4) Reorder the terms: -14 + 18t = -10 + 5t + -1(-4 + 3t) -14 + 18t = -10 + 5t + (-4 * -1 + 3t * -1) -14 + 18t = -10 + 5t + (4 + -3t) Reorder the terms: -14 + 18t = -10 + 4 + 5t + -3t Combine like terms: -10 + 4 = -6 -14 + 18t = -6 + 5t + -3t Combine like terms: 5t + -3t = 2t -14 + 18t = -6 + 2t Solving -14 + 18t = -6 + 2t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2t' to each side of the equation. -14 + 18t + -2t = -6 + 2t + -2t Combine like terms: 18t + -2t = 16t -14 + 16t = -6 + 2t + -2t Combine like terms: 2t + -2t = 0 -14 + 16t = -6 + 0 -14 + 16t = -6 Add '14' to each side of the equation. -14 + 14 + 16t = -6 + 14 Combine like terms: -14 + 14 = 0 0 + 16t = -6 + 14 16t = -6 + 14 Combine like terms: -6 + 14 = 8 16t = 8 Divide each side by '16'. t = 0.5 Simplifying t = 0.5

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