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Simplifying -9(t + 6) + 7(1 + -3t) = -31(t + 2) + -9 Reorder the terms: -9(6 + t) + 7(1 + -3t) = -31(t + 2) + -9 (6 * -9 + t * -9) + 7(1 + -3t) = -31(t + 2) + -9 (-54 + -9t) + 7(1 + -3t) = -31(t + 2) + -9 -54 + -9t + (1 * 7 + -3t * 7) = -31(t + 2) + -9 -54 + -9t + (7 + -21t) = -31(t + 2) + -9 Reorder the terms: -54 + 7 + -9t + -21t = -31(t + 2) + -9 Combine like terms: -54 + 7 = -47 -47 + -9t + -21t = -31(t + 2) + -9 Combine like terms: -9t + -21t = -30t -47 + -30t = -31(t + 2) + -9 Reorder the terms: -47 + -30t = -31(2 + t) + -9 -47 + -30t = (2 * -31 + t * -31) + -9 -47 + -30t = (-62 + -31t) + -9 Reorder the terms: -47 + -30t = -62 + -9 + -31t Combine like terms: -62 + -9 = -71 -47 + -30t = -71 + -31t Solving -47 + -30t = -71 + -31t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '31t' to each side of the equation. -47 + -30t + 31t = -71 + -31t + 31t Combine like terms: -30t + 31t = 1t -47 + 1t = -71 + -31t + 31t Combine like terms: -31t + 31t = 0 -47 + 1t = -71 + 0 -47 + 1t = -71 Add '47' to each side of the equation. -47 + 47 + 1t = -71 + 47 Combine like terms: -47 + 47 = 0 0 + 1t = -71 + 47 1t = -71 + 47 Combine like terms: -71 + 47 = -24 1t = -24 Divide each side by '1'. t = -24 Simplifying t = -24
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