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Simplifying 4(9 + -1t) + 6 = -6(t + -3) + -9 (9 * 4 + -1t * 4) + 6 = -6(t + -3) + -9 (36 + -4t) + 6 = -6(t + -3) + -9 Reorder the terms: 36 + 6 + -4t = -6(t + -3) + -9 Combine like terms: 36 + 6 = 42 42 + -4t = -6(t + -3) + -9 Reorder the terms: 42 + -4t = -6(-3 + t) + -9 42 + -4t = (-3 * -6 + t * -6) + -9 42 + -4t = (18 + -6t) + -9 Reorder the terms: 42 + -4t = 18 + -9 + -6t Combine like terms: 18 + -9 = 9 42 + -4t = 9 + -6t Solving 42 + -4t = 9 + -6t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6t' to each side of the equation. 42 + -4t + 6t = 9 + -6t + 6t Combine like terms: -4t + 6t = 2t 42 + 2t = 9 + -6t + 6t Combine like terms: -6t + 6t = 0 42 + 2t = 9 + 0 42 + 2t = 9 Add '-42' to each side of the equation. 42 + -42 + 2t = 9 + -42 Combine like terms: 42 + -42 = 0 0 + 2t = 9 + -42 2t = 9 + -42 Combine like terms: 9 + -42 = -33 2t = -33 Divide each side by '2'. t = -16.5 Simplifying t = -16.5
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