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Simplifying 8(t + 2) + -3(t + -4) = 6(t + -7) + 8 Reorder the terms: 8(2 + t) + -3(t + -4) = 6(t + -7) + 8 (2 * 8 + t * 8) + -3(t + -4) = 6(t + -7) + 8 (16 + 8t) + -3(t + -4) = 6(t + -7) + 8 Reorder the terms: 16 + 8t + -3(-4 + t) = 6(t + -7) + 8 16 + 8t + (-4 * -3 + t * -3) = 6(t + -7) + 8 16 + 8t + (12 + -3t) = 6(t + -7) + 8 Reorder the terms: 16 + 12 + 8t + -3t = 6(t + -7) + 8 Combine like terms: 16 + 12 = 28 28 + 8t + -3t = 6(t + -7) + 8 Combine like terms: 8t + -3t = 5t 28 + 5t = 6(t + -7) + 8 Reorder the terms: 28 + 5t = 6(-7 + t) + 8 28 + 5t = (-7 * 6 + t * 6) + 8 28 + 5t = (-42 + 6t) + 8 Reorder the terms: 28 + 5t = -42 + 8 + 6t Combine like terms: -42 + 8 = -34 28 + 5t = -34 + 6t Solving 28 + 5t = -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. 28 + 5t + -6t = -34 + 6t + -6t Combine like terms: 5t + -6t = -1t 28 + -1t = -34 + 6t + -6t Combine like terms: 6t + -6t = 0 28 + -1t = -34 + 0 28 + -1t = -34 Add '-28' to each side of the equation. 28 + -28 + -1t = -34 + -28 Combine like terms: 28 + -28 = 0 0 + -1t = -34 + -28 -1t = -34 + -28 Combine like terms: -34 + -28 = -62 -1t = -62 Divide each side by '-1'. t = 62 Simplifying t = 62
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