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Simplifying 5(9 + -1t) + 3 = -3(t + -2) + -6 (9 * 5 + -1t * 5) + 3 = -3(t + -2) + -6 (45 + -5t) + 3 = -3(t + -2) + -6 Reorder the terms: 45 + 3 + -5t = -3(t + -2) + -6 Combine like terms: 45 + 3 = 48 48 + -5t = -3(t + -2) + -6 Reorder the terms: 48 + -5t = -3(-2 + t) + -6 48 + -5t = (-2 * -3 + t * -3) + -6 48 + -5t = (6 + -3t) + -6 Reorder the terms: 48 + -5t = 6 + -6 + -3t Combine like terms: 6 + -6 = 0 48 + -5t = 0 + -3t 48 + -5t = -3t Solving 48 + -5t = -3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3t' to each side of the equation. 48 + -5t + 3t = -3t + 3t Combine like terms: -5t + 3t = -2t 48 + -2t = -3t + 3t Combine like terms: -3t + 3t = 0 48 + -2t = 0 Add '-48' to each side of the equation. 48 + -48 + -2t = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -2t = 0 + -48 -2t = 0 + -48 Combine like terms: 0 + -48 = -48 -2t = -48 Divide each side by '-2'. t = 24 Simplifying t = 24
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