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Simplifying 5(t + -9) + -6(2t + 1) = -8(t + 4) + -2 Reorder the terms: 5(-9 + t) + -6(2t + 1) = -8(t + 4) + -2 (-9 * 5 + t * 5) + -6(2t + 1) = -8(t + 4) + -2 (-45 + 5t) + -6(2t + 1) = -8(t + 4) + -2 Reorder the terms: -45 + 5t + -6(1 + 2t) = -8(t + 4) + -2 -45 + 5t + (1 * -6 + 2t * -6) = -8(t + 4) + -2 -45 + 5t + (-6 + -12t) = -8(t + 4) + -2 Reorder the terms: -45 + -6 + 5t + -12t = -8(t + 4) + -2 Combine like terms: -45 + -6 = -51 -51 + 5t + -12t = -8(t + 4) + -2 Combine like terms: 5t + -12t = -7t -51 + -7t = -8(t + 4) + -2 Reorder the terms: -51 + -7t = -8(4 + t) + -2 -51 + -7t = (4 * -8 + t * -8) + -2 -51 + -7t = (-32 + -8t) + -2 Reorder the terms: -51 + -7t = -32 + -2 + -8t Combine like terms: -32 + -2 = -34 -51 + -7t = -34 + -8t Solving -51 + -7t = -34 + -8t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8t' to each side of the equation. -51 + -7t + 8t = -34 + -8t + 8t Combine like terms: -7t + 8t = 1t -51 + 1t = -34 + -8t + 8t Combine like terms: -8t + 8t = 0 -51 + 1t = -34 + 0 -51 + 1t = -34 Add '51' to each side of the equation. -51 + 51 + 1t = -34 + 51 Combine like terms: -51 + 51 = 0 0 + 1t = -34 + 51 1t = -34 + 51 Combine like terms: -34 + 51 = 17 1t = 17 Divide each side by '1'. t = 17 Simplifying t = 17
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