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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 + 8t + 12 + -3t + 6(-7 + t) = 8 16 + 8t + 12 + -3t + (-7 * 6 + t * 6) = 8 16 + 8t + 12 + -3t + (-42 + 6t) = 8 Reorder the terms: 16 + 12 + -42 + 8t + -3t + 6t = 8 Combine like terms: 16 + 12 = 28 28 + -42 + 8t + -3t + 6t = 8 Combine like terms: 28 + -42 = -14 -14 + 8t + -3t + 6t = 8 Combine like terms: 8t + -3t = 5t -14 + 5t + 6t = 8 Combine like terms: 5t + 6t = 11t -14 + 11t = 8 Solving -14 + 11t = 8 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + 11t = 8 + 14 Combine like terms: -14 + 14 = 0 0 + 11t = 8 + 14 11t = 8 + 14 Combine like terms: 8 + 14 = 22 11t = 22 Divide each side by '11'. t = 2 Simplifying t = 2
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