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Simplifying 5[3(7 + -1t) + -4(8 + 2t)] = 6[2(6 + 3t) + -4] 5[(7 * 3 + -1t * 3) + -4(8 + 2t)] = 6[2(6 + 3t) + -4] 5[(21 + -3t) + -4(8 + 2t)] = 6[2(6 + 3t) + -4] 5[21 + -3t + (8 * -4 + 2t * -4)] = 6[2(6 + 3t) + -4] 5[21 + -3t + (-32 + -8t)] = 6[2(6 + 3t) + -4] Reorder the terms: 5[21 + -32 + -3t + -8t] = 6[2(6 + 3t) + -4] Combine like terms: 21 + -32 = -11 5[-11 + -3t + -8t] = 6[2(6 + 3t) + -4] Combine like terms: -3t + -8t = -11t 5[-11 + -11t] = 6[2(6 + 3t) + -4] [-11 * 5 + -11t * 5] = 6[2(6 + 3t) + -4] [-55 + -55t] = 6[2(6 + 3t) + -4] -55 + -55t = 6[(6 * 2 + 3t * 2) + -4] -55 + -55t = 6[(12 + 6t) + -4] Reorder the terms: -55 + -55t = 6[12 + -4 + 6t] Combine like terms: 12 + -4 = 8 -55 + -55t = 6[8 + 6t] -55 + -55t = [8 * 6 + 6t * 6] -55 + -55t = [48 + 36t] Solving -55 + -55t = 48 + 36t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-36t' to each side of the equation. -55 + -55t + -36t = 48 + 36t + -36t Combine like terms: -55t + -36t = -91t -55 + -91t = 48 + 36t + -36t Combine like terms: 36t + -36t = 0 -55 + -91t = 48 + 0 -55 + -91t = 48 Add '55' to each side of the equation. -55 + 55 + -91t = 48 + 55 Combine like terms: -55 + 55 = 0 0 + -91t = 48 + 55 -91t = 48 + 55 Combine like terms: 48 + 55 = 103 -91t = 103 Divide each side by '-91'. t = -1.131868132 Simplifying t = -1.131868132
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