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Simplifying 2(t + -2) + -3(3t + -4) = 13 + -5(7t + 4) Reorder the terms: 2(-2 + t) + -3(3t + -4) = 13 + -5(7t + 4) (-2 * 2 + t * 2) + -3(3t + -4) = 13 + -5(7t + 4) (-4 + 2t) + -3(3t + -4) = 13 + -5(7t + 4) Reorder the terms: -4 + 2t + -3(-4 + 3t) = 13 + -5(7t + 4) -4 + 2t + (-4 * -3 + 3t * -3) = 13 + -5(7t + 4) -4 + 2t + (12 + -9t) = 13 + -5(7t + 4) Reorder the terms: -4 + 12 + 2t + -9t = 13 + -5(7t + 4) Combine like terms: -4 + 12 = 8 8 + 2t + -9t = 13 + -5(7t + 4) Combine like terms: 2t + -9t = -7t 8 + -7t = 13 + -5(7t + 4) Reorder the terms: 8 + -7t = 13 + -5(4 + 7t) 8 + -7t = 13 + (4 * -5 + 7t * -5) 8 + -7t = 13 + (-20 + -35t) Combine like terms: 13 + -20 = -7 8 + -7t = -7 + -35t Solving 8 + -7t = -7 + -35t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35t' to each side of the equation. 8 + -7t + 35t = -7 + -35t + 35t Combine like terms: -7t + 35t = 28t 8 + 28t = -7 + -35t + 35t Combine like terms: -35t + 35t = 0 8 + 28t = -7 + 0 8 + 28t = -7 Add '-8' to each side of the equation. 8 + -8 + 28t = -7 + -8 Combine like terms: 8 + -8 = 0 0 + 28t = -7 + -8 28t = -7 + -8 Combine like terms: -7 + -8 = -15 28t = -15 Divide each side by '28'. t = -0.5357142857 Simplifying t = -0.5357142857
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