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Simplifying 4(3t + -5) + 11(2t + 4) = 7(2t + -8) + 1 Reorder the terms: 4(-5 + 3t) + 11(2t + 4) = 7(2t + -8) + 1 (-5 * 4 + 3t * 4) + 11(2t + 4) = 7(2t + -8) + 1 (-20 + 12t) + 11(2t + 4) = 7(2t + -8) + 1 Reorder the terms: -20 + 12t + 11(4 + 2t) = 7(2t + -8) + 1 -20 + 12t + (4 * 11 + 2t * 11) = 7(2t + -8) + 1 -20 + 12t + (44 + 22t) = 7(2t + -8) + 1 Reorder the terms: -20 + 44 + 12t + 22t = 7(2t + -8) + 1 Combine like terms: -20 + 44 = 24 24 + 12t + 22t = 7(2t + -8) + 1 Combine like terms: 12t + 22t = 34t 24 + 34t = 7(2t + -8) + 1 Reorder the terms: 24 + 34t = 7(-8 + 2t) + 1 24 + 34t = (-8 * 7 + 2t * 7) + 1 24 + 34t = (-56 + 14t) + 1 Reorder the terms: 24 + 34t = -56 + 1 + 14t Combine like terms: -56 + 1 = -55 24 + 34t = -55 + 14t Solving 24 + 34t = -55 + 14t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14t' to each side of the equation. 24 + 34t + -14t = -55 + 14t + -14t Combine like terms: 34t + -14t = 20t 24 + 20t = -55 + 14t + -14t Combine like terms: 14t + -14t = 0 24 + 20t = -55 + 0 24 + 20t = -55 Add '-24' to each side of the equation. 24 + -24 + 20t = -55 + -24 Combine like terms: 24 + -24 = 0 0 + 20t = -55 + -24 20t = -55 + -24 Combine like terms: -55 + -24 = -79 20t = -79 Divide each side by '20'. t = -3.95 Simplifying t = -3.95
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