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Simplifying 2(t + -2) + -5(3t + -4) = 14 + -8(4t + 1) Reorder the terms: 2(-2 + t) + -5(3t + -4) = 14 + -8(4t + 1) (-2 * 2 + t * 2) + -5(3t + -4) = 14 + -8(4t + 1) (-4 + 2t) + -5(3t + -4) = 14 + -8(4t + 1) Reorder the terms: -4 + 2t + -5(-4 + 3t) = 14 + -8(4t + 1) -4 + 2t + (-4 * -5 + 3t * -5) = 14 + -8(4t + 1) -4 + 2t + (20 + -15t) = 14 + -8(4t + 1) Reorder the terms: -4 + 20 + 2t + -15t = 14 + -8(4t + 1) Combine like terms: -4 + 20 = 16 16 + 2t + -15t = 14 + -8(4t + 1) Combine like terms: 2t + -15t = -13t 16 + -13t = 14 + -8(4t + 1) Reorder the terms: 16 + -13t = 14 + -8(1 + 4t) 16 + -13t = 14 + (1 * -8 + 4t * -8) 16 + -13t = 14 + (-8 + -32t) Combine like terms: 14 + -8 = 6 16 + -13t = 6 + -32t Solving 16 + -13t = 6 + -32t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '32t' to each side of the equation. 16 + -13t + 32t = 6 + -32t + 32t Combine like terms: -13t + 32t = 19t 16 + 19t = 6 + -32t + 32t Combine like terms: -32t + 32t = 0 16 + 19t = 6 + 0 16 + 19t = 6 Add '-16' to each side of the equation. 16 + -16 + 19t = 6 + -16 Combine like terms: 16 + -16 = 0 0 + 19t = 6 + -16 19t = 6 + -16 Combine like terms: 6 + -16 = -10 19t = -10 Divide each side by '19'. t = -0.5263157895 Simplifying t = -0.5263157895
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