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Simplifying -5(t + 9) + 4(2t + 4) = 2(t + -8) + 6 Reorder the terms: -5(9 + t) + 4(2t + 4) = 2(t + -8) + 6 (9 * -5 + t * -5) + 4(2t + 4) = 2(t + -8) + 6 (-45 + -5t) + 4(2t + 4) = 2(t + -8) + 6 Reorder the terms: -45 + -5t + 4(4 + 2t) = 2(t + -8) + 6 -45 + -5t + (4 * 4 + 2t * 4) = 2(t + -8) + 6 -45 + -5t + (16 + 8t) = 2(t + -8) + 6 Reorder the terms: -45 + 16 + -5t + 8t = 2(t + -8) + 6 Combine like terms: -45 + 16 = -29 -29 + -5t + 8t = 2(t + -8) + 6 Combine like terms: -5t + 8t = 3t -29 + 3t = 2(t + -8) + 6 Reorder the terms: -29 + 3t = 2(-8 + t) + 6 -29 + 3t = (-8 * 2 + t * 2) + 6 -29 + 3t = (-16 + 2t) + 6 Reorder the terms: -29 + 3t = -16 + 6 + 2t Combine like terms: -16 + 6 = -10 -29 + 3t = -10 + 2t Solving -29 + 3t = -10 + 2t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2t' to each side of the equation. -29 + 3t + -2t = -10 + 2t + -2t Combine like terms: 3t + -2t = 1t -29 + 1t = -10 + 2t + -2t Combine like terms: 2t + -2t = 0 -29 + 1t = -10 + 0 -29 + 1t = -10 Add '29' to each side of the equation. -29 + 29 + 1t = -10 + 29 Combine like terms: -29 + 29 = 0 0 + 1t = -10 + 29 1t = -10 + 29 Combine like terms: -10 + 29 = 19 1t = 19 Divide each side by '1'. t = 19 Simplifying t = 19
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