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Simplifying 8(t + -4) + -6(4t + 3) = -17(t + 5) + 7 Reorder the terms: 8(-4 + t) + -6(4t + 3) = -17(t + 5) + 7 (-4 * 8 + t * 8) + -6(4t + 3) = -17(t + 5) + 7 (-32 + 8t) + -6(4t + 3) = -17(t + 5) + 7 Reorder the terms: -32 + 8t + -6(3 + 4t) = -17(t + 5) + 7 -32 + 8t + (3 * -6 + 4t * -6) = -17(t + 5) + 7 -32 + 8t + (-18 + -24t) = -17(t + 5) + 7 Reorder the terms: -32 + -18 + 8t + -24t = -17(t + 5) + 7 Combine like terms: -32 + -18 = -50 -50 + 8t + -24t = -17(t + 5) + 7 Combine like terms: 8t + -24t = -16t -50 + -16t = -17(t + 5) + 7 Reorder the terms: -50 + -16t = -17(5 + t) + 7 -50 + -16t = (5 * -17 + t * -17) + 7 -50 + -16t = (-85 + -17t) + 7 Reorder the terms: -50 + -16t = -85 + 7 + -17t Combine like terms: -85 + 7 = -78 -50 + -16t = -78 + -17t Solving -50 + -16t = -78 + -17t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17t' to each side of the equation. -50 + -16t + 17t = -78 + -17t + 17t Combine like terms: -16t + 17t = 1t -50 + 1t = -78 + -17t + 17t Combine like terms: -17t + 17t = 0 -50 + 1t = -78 + 0 -50 + 1t = -78 Add '50' to each side of the equation. -50 + 50 + 1t = -78 + 50 Combine like terms: -50 + 50 = 0 0 + 1t = -78 + 50 1t = -78 + 50 Combine like terms: -78 + 50 = -28 1t = -28 Divide each side by '1'. t = -28 Simplifying t = -28
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