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Simplifying 2(t + -4) + -3(2t + -7) = 3 + -5(3t + 1) Reorder the terms: 2(-4 + t) + -3(2t + -7) = 3 + -5(3t + 1) (-4 * 2 + t * 2) + -3(2t + -7) = 3 + -5(3t + 1) (-8 + 2t) + -3(2t + -7) = 3 + -5(3t + 1) Reorder the terms: -8 + 2t + -3(-7 + 2t) = 3 + -5(3t + 1) -8 + 2t + (-7 * -3 + 2t * -3) = 3 + -5(3t + 1) -8 + 2t + (21 + -6t) = 3 + -5(3t + 1) Reorder the terms: -8 + 21 + 2t + -6t = 3 + -5(3t + 1) Combine like terms: -8 + 21 = 13 13 + 2t + -6t = 3 + -5(3t + 1) Combine like terms: 2t + -6t = -4t 13 + -4t = 3 + -5(3t + 1) Reorder the terms: 13 + -4t = 3 + -5(1 + 3t) 13 + -4t = 3 + (1 * -5 + 3t * -5) 13 + -4t = 3 + (-5 + -15t) Combine like terms: 3 + -5 = -2 13 + -4t = -2 + -15t Solving 13 + -4t = -2 + -15t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15t' to each side of the equation. 13 + -4t + 15t = -2 + -15t + 15t Combine like terms: -4t + 15t = 11t 13 + 11t = -2 + -15t + 15t Combine like terms: -15t + 15t = 0 13 + 11t = -2 + 0 13 + 11t = -2 Add '-13' to each side of the equation. 13 + -13 + 11t = -2 + -13 Combine like terms: 13 + -13 = 0 0 + 11t = -2 + -13 11t = -2 + -13 Combine like terms: -2 + -13 = -15 11t = -15 Divide each side by '11'. t = -1.363636364 Simplifying t = -1.363636364
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