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Simplifying 8(t + 2) + -3(2 + -4) = 6(t + -7) + 8 Reorder the terms: 8(2 + t) + -3(2 + -4) = 6(t + -7) + 8 (2 * 8 + t * 8) + -3(2 + -4) = 6(t + -7) + 8 (16 + 8t) + -3(2 + -4) = 6(t + -7) + 8 Combine like terms: 2 + -4 = -2 16 + 8t + -3(-2) = 6(t + -7) + 8 Multiply -3 * -2 16 + 8t + 6 = 6(t + -7) + 8 Reorder the terms: 16 + 6 + 8t = 6(t + -7) + 8 Combine like terms: 16 + 6 = 22 22 + 8t = 6(t + -7) + 8 Reorder the terms: 22 + 8t = 6(-7 + t) + 8 22 + 8t = (-7 * 6 + t * 6) + 8 22 + 8t = (-42 + 6t) + 8 Reorder the terms: 22 + 8t = -42 + 8 + 6t Combine like terms: -42 + 8 = -34 22 + 8t = -34 + 6t Solving 22 + 8t = -34 + 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. 22 + 8t + -6t = -34 + 6t + -6t Combine like terms: 8t + -6t = 2t 22 + 2t = -34 + 6t + -6t Combine like terms: 6t + -6t = 0 22 + 2t = -34 + 0 22 + 2t = -34 Add '-22' to each side of the equation. 22 + -22 + 2t = -34 + -22 Combine like terms: 22 + -22 = 0 0 + 2t = -34 + -22 2t = -34 + -22 Combine like terms: -34 + -22 = -56 2t = -56 Divide each side by '2'. t = -28 Simplifying t = -28
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