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Simplifying 3(t + -3) + -1(4t + -1) = 2(5t + -2) + 29 Reorder the terms: 3(-3 + t) + -1(4t + -1) = 2(5t + -2) + 29 (-3 * 3 + t * 3) + -1(4t + -1) = 2(5t + -2) + 29 (-9 + 3t) + -1(4t + -1) = 2(5t + -2) + 29 Reorder the terms: -9 + 3t + -1(-1 + 4t) = 2(5t + -2) + 29 -9 + 3t + (-1 * -1 + 4t * -1) = 2(5t + -2) + 29 -9 + 3t + (1 + -4t) = 2(5t + -2) + 29 Reorder the terms: -9 + 1 + 3t + -4t = 2(5t + -2) + 29 Combine like terms: -9 + 1 = -8 -8 + 3t + -4t = 2(5t + -2) + 29 Combine like terms: 3t + -4t = -1t -8 + -1t = 2(5t + -2) + 29 Reorder the terms: -8 + -1t = 2(-2 + 5t) + 29 -8 + -1t = (-2 * 2 + 5t * 2) + 29 -8 + -1t = (-4 + 10t) + 29 Reorder the terms: -8 + -1t = -4 + 29 + 10t Combine like terms: -4 + 29 = 25 -8 + -1t = 25 + 10t Solving -8 + -1t = 25 + 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. -8 + -1t + -10t = 25 + 10t + -10t Combine like terms: -1t + -10t = -11t -8 + -11t = 25 + 10t + -10t Combine like terms: 10t + -10t = 0 -8 + -11t = 25 + 0 -8 + -11t = 25 Add '8' to each side of the equation. -8 + 8 + -11t = 25 + 8 Combine like terms: -8 + 8 = 0 0 + -11t = 25 + 8 -11t = 25 + 8 Combine like terms: 25 + 8 = 33 -11t = 33 Divide each side by '-11'. t = -3 Simplifying t = -3
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