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