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Simplifying 6(t + -5) + 2(2t + 1) = 9(t + -4) + 2 Reorder the terms: 6(-5 + t) + 2(2t + 1) = 9(t + -4) + 2 (-5 * 6 + t * 6) + 2(2t + 1) = 9(t + -4) + 2 (-30 + 6t) + 2(2t + 1) = 9(t + -4) + 2 Reorder the terms: -30 + 6t + 2(1 + 2t) = 9(t + -4) + 2 -30 + 6t + (1 * 2 + 2t * 2) = 9(t + -4) + 2 -30 + 6t + (2 + 4t) = 9(t + -4) + 2 Reorder the terms: -30 + 2 + 6t + 4t = 9(t + -4) + 2 Combine like terms: -30 + 2 = -28 -28 + 6t + 4t = 9(t + -4) + 2 Combine like terms: 6t + 4t = 10t -28 + 10t = 9(t + -4) + 2 Reorder the terms: -28 + 10t = 9(-4 + t) + 2 -28 + 10t = (-4 * 9 + t * 9) + 2 -28 + 10t = (-36 + 9t) + 2 Reorder the terms: -28 + 10t = -36 + 2 + 9t Combine like terms: -36 + 2 = -34 -28 + 10t = -34 + 9t Solving -28 + 10t = -34 + 9t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9t' to each side of the equation. -28 + 10t + -9t = -34 + 9t + -9t Combine like terms: 10t + -9t = 1t -28 + 1t = -34 + 9t + -9t Combine like terms: 9t + -9t = 0 -28 + 1t = -34 + 0 -28 + 1t = -34 Add '28' to each side of the equation. -28 + 28 + 1t = -34 + 28 Combine like terms: -28 + 28 = 0 0 + 1t = -34 + 28 1t = -34 + 28 Combine like terms: -34 + 28 = -6 1t = -6 Divide each side by '1'. t = -6 Simplifying t = -6
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