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Simplifying 8(t + -4) + -4(4t + 7) = -9(t + 7) + 4 Reorder the terms: 8(-4 + t) + -4(4t + 7) = -9(t + 7) + 4 (-4 * 8 + t * 8) + -4(4t + 7) = -9(t + 7) + 4 (-32 + 8t) + -4(4t + 7) = -9(t + 7) + 4 Reorder the terms: -32 + 8t + -4(7 + 4t) = -9(t + 7) + 4 -32 + 8t + (7 * -4 + 4t * -4) = -9(t + 7) + 4 -32 + 8t + (-28 + -16t) = -9(t + 7) + 4 Reorder the terms: -32 + -28 + 8t + -16t = -9(t + 7) + 4 Combine like terms: -32 + -28 = -60 -60 + 8t + -16t = -9(t + 7) + 4 Combine like terms: 8t + -16t = -8t -60 + -8t = -9(t + 7) + 4 Reorder the terms: -60 + -8t = -9(7 + t) + 4 -60 + -8t = (7 * -9 + t * -9) + 4 -60 + -8t = (-63 + -9t) + 4 Reorder the terms: -60 + -8t = -63 + 4 + -9t Combine like terms: -63 + 4 = -59 -60 + -8t = -59 + -9t Solving -60 + -8t = -59 + -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. -60 + -8t + 9t = -59 + -9t + 9t Combine like terms: -8t + 9t = 1t -60 + 1t = -59 + -9t + 9t Combine like terms: -9t + 9t = 0 -60 + 1t = -59 + 0 -60 + 1t = -59 Add '60' to each side of the equation. -60 + 60 + 1t = -59 + 60 Combine like terms: -60 + 60 = 0 0 + 1t = -59 + 60 1t = -59 + 60 Combine like terms: -59 + 60 = 1 1t = 1 Divide each side by '1'. t = 1 Simplifying t = 1
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