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Simplifying 2[4t + 7 + -3(2t + 3)] = 8(3t + -4) + -7(2t + -3) Reorder the terms: 2[4t + 7 + -3(3 + 2t)] = 8(3t + -4) + -7(2t + -3) 2[4t + 7 + (3 * -3 + 2t * -3)] = 8(3t + -4) + -7(2t + -3) 2[4t + 7 + (-9 + -6t)] = 8(3t + -4) + -7(2t + -3) Reorder the terms: 2[7 + -9 + 4t + -6t] = 8(3t + -4) + -7(2t + -3) Combine like terms: 7 + -9 = -2 2[-2 + 4t + -6t] = 8(3t + -4) + -7(2t + -3) Combine like terms: 4t + -6t = -2t 2[-2 + -2t] = 8(3t + -4) + -7(2t + -3) [-2 * 2 + -2t * 2] = 8(3t + -4) + -7(2t + -3) [-4 + -4t] = 8(3t + -4) + -7(2t + -3) Reorder the terms: -4 + -4t = 8(-4 + 3t) + -7(2t + -3) -4 + -4t = (-4 * 8 + 3t * 8) + -7(2t + -3) -4 + -4t = (-32 + 24t) + -7(2t + -3) Reorder the terms: -4 + -4t = -32 + 24t + -7(-3 + 2t) -4 + -4t = -32 + 24t + (-3 * -7 + 2t * -7) -4 + -4t = -32 + 24t + (21 + -14t) Reorder the terms: -4 + -4t = -32 + 21 + 24t + -14t Combine like terms: -32 + 21 = -11 -4 + -4t = -11 + 24t + -14t Combine like terms: 24t + -14t = 10t -4 + -4t = -11 + 10t Solving -4 + -4t = -11 + 10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10t' to each side of the equation. -4 + -4t + -10t = -11 + 10t + -10t Combine like terms: -4t + -10t = -14t -4 + -14t = -11 + 10t + -10t Combine like terms: 10t + -10t = 0 -4 + -14t = -11 + 0 -4 + -14t = -11 Add '4' to each side of the equation. -4 + 4 + -14t = -11 + 4 Combine like terms: -4 + 4 = 0 0 + -14t = -11 + 4 -14t = -11 + 4 Combine like terms: -11 + 4 = -7 -14t = -7 Divide each side by '-14'. t = 0.5 Simplifying t = 0.5
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