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Simplifying 5.12t + 12.42(30 + -1t) = 500 5.12t + (30 * 12.42 + -1t * 12.42) = 500 5.12t + (372.6 + -12.42t) = 500 Reorder the terms: 372.6 + 5.12t + -12.42t = 500 Combine like terms: 5.12t + -12.42t = -7.3t 372.6 + -7.3t = 500 Solving 372.6 + -7.3t = 500 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-372.6' to each side of the equation. 372.6 + -372.6 + -7.3t = 500 + -372.6 Combine like terms: 372.6 + -372.6 = 0.0 0.0 + -7.3t = 500 + -372.6 -7.3t = 500 + -372.6 Combine like terms: 500 + -372.6 = 127.4 -7.3t = 127.4 Divide each side by '-7.3'. t = -17.45205479 Simplifying t = -17.45205479
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