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Simplifying -3(t + 4) + -2(8t + 5) = -20(t + 1) + 4 Reorder the terms: -3(4 + t) + -2(8t + 5) = -20(t + 1) + 4 (4 * -3 + t * -3) + -2(8t + 5) = -20(t + 1) + 4 (-12 + -3t) + -2(8t + 5) = -20(t + 1) + 4 Reorder the terms: -12 + -3t + -2(5 + 8t) = -20(t + 1) + 4 -12 + -3t + (5 * -2 + 8t * -2) = -20(t + 1) + 4 -12 + -3t + (-10 + -16t) = -20(t + 1) + 4 Reorder the terms: -12 + -10 + -3t + -16t = -20(t + 1) + 4 Combine like terms: -12 + -10 = -22 -22 + -3t + -16t = -20(t + 1) + 4 Combine like terms: -3t + -16t = -19t -22 + -19t = -20(t + 1) + 4 Reorder the terms: -22 + -19t = -20(1 + t) + 4 -22 + -19t = (1 * -20 + t * -20) + 4 -22 + -19t = (-20 + -20t) + 4 Reorder the terms: -22 + -19t = -20 + 4 + -20t Combine like terms: -20 + 4 = -16 -22 + -19t = -16 + -20t Solving -22 + -19t = -16 + -20t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20t' to each side of the equation. -22 + -19t + 20t = -16 + -20t + 20t Combine like terms: -19t + 20t = 1t -22 + 1t = -16 + -20t + 20t Combine like terms: -20t + 20t = 0 -22 + 1t = -16 + 0 -22 + 1t = -16 Add '22' to each side of the equation. -22 + 22 + 1t = -16 + 22 Combine like terms: -22 + 22 = 0 0 + 1t = -16 + 22 1t = -16 + 22 Combine like terms: -16 + 22 = 6 1t = 6 Divide each side by '1'. t = 6 Simplifying t = 6
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