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Simplifying 9t + 0.5(10 + -8t) = -3t + 6 9t + (10 * 0.5 + -8t * 0.5) = -3t + 6 9t + (5 + -4t) = -3t + 6 Reorder the terms: 5 + 9t + -4t = -3t + 6 Combine like terms: 9t + -4t = 5t 5 + 5t = -3t + 6 Reorder the terms: 5 + 5t = 6 + -3t Solving 5 + 5t = 6 + -3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3t' to each side of the equation. 5 + 5t + 3t = 6 + -3t + 3t Combine like terms: 5t + 3t = 8t 5 + 8t = 6 + -3t + 3t Combine like terms: -3t + 3t = 0 5 + 8t = 6 + 0 5 + 8t = 6 Add '-5' to each side of the equation. 5 + -5 + 8t = 6 + -5 Combine like terms: 5 + -5 = 0 0 + 8t = 6 + -5 8t = 6 + -5 Combine like terms: 6 + -5 = 1 8t = 1 Divide each side by '8'. t = 0.125 Simplifying t = 0.125
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