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Simplifying 15t + 4(2t + 3) = 10 + -1[4t + 2(t + -7)] Reorder the terms: 15t + 4(3 + 2t) = 10 + -1[4t + 2(t + -7)] 15t + (3 * 4 + 2t * 4) = 10 + -1[4t + 2(t + -7)] 15t + (12 + 8t) = 10 + -1[4t + 2(t + -7)] Reorder the terms: 12 + 15t + 8t = 10 + -1[4t + 2(t + -7)] Combine like terms: 15t + 8t = 23t 12 + 23t = 10 + -1[4t + 2(t + -7)] Reorder the terms: 12 + 23t = 10 + -1[4t + 2(-7 + t)] 12 + 23t = 10 + -1[4t + (-7 * 2 + t * 2)] 12 + 23t = 10 + -1[4t + (-14 + 2t)] Reorder the terms: 12 + 23t = 10 + -1[-14 + 4t + 2t] Combine like terms: 4t + 2t = 6t 12 + 23t = 10 + -1[-14 + 6t] 12 + 23t = 10 + [-14 * -1 + 6t * -1] 12 + 23t = 10 + [14 + -6t] Combine like terms: 10 + 14 = 24 12 + 23t = 24 + -6t Solving 12 + 23t = 24 + -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. 12 + 23t + 6t = 24 + -6t + 6t Combine like terms: 23t + 6t = 29t 12 + 29t = 24 + -6t + 6t Combine like terms: -6t + 6t = 0 12 + 29t = 24 + 0 12 + 29t = 24 Add '-12' to each side of the equation. 12 + -12 + 29t = 24 + -12 Combine like terms: 12 + -12 = 0 0 + 29t = 24 + -12 29t = 24 + -12 Combine like terms: 24 + -12 = 12 29t = 12 Divide each side by '29'. t = 0.4137931034 Simplifying t = 0.4137931034
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