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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 Reorder the terms for easier multiplication: 28 + 5t = 6 * 8(-7 + t) Multiply 6 * 8 28 + 5t = 48(-7 + t) 28 + 5t = (-7 * 48 + t * 48) 28 + 5t = (-336 + 48t) Solving 28 + 5t = -336 + 48t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-48t' to each side of the equation. 28 + 5t + -48t = -336 + 48t + -48t Combine like terms: 5t + -48t = -43t 28 + -43t = -336 + 48t + -48t Combine like terms: 48t + -48t = 0 28 + -43t = -336 + 0 28 + -43t = -336 Add '-28' to each side of the equation. 28 + -28 + -43t = -336 + -28 Combine like terms: 28 + -28 = 0 0 + -43t = -336 + -28 -43t = -336 + -28 Combine like terms: -336 + -28 = -364 -43t = -364 Divide each side by '-43'. t = 8.465116279 Simplifying t = 8.465116279
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