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Simplifying 8(2 + 1) + -1(t + -9) = -52 + -8t Combine like terms: 2 + 1 = 3 8(3) + -1(t + -9) = -52 + -8t Multiply 8 * 3 24 + -1(t + -9) = -52 + -8t Reorder the terms: 24 + -1(-9 + t) = -52 + -8t 24 + (-9 * -1 + t * -1) = -52 + -8t 24 + (9 + -1t) = -52 + -8t Combine like terms: 24 + 9 = 33 33 + -1t = -52 + -8t Solving 33 + -1t = -52 + -8t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8t' to each side of the equation. 33 + -1t + 8t = -52 + -8t + 8t Combine like terms: -1t + 8t = 7t 33 + 7t = -52 + -8t + 8t Combine like terms: -8t + 8t = 0 33 + 7t = -52 + 0 33 + 7t = -52 Add '-33' to each side of the equation. 33 + -33 + 7t = -52 + -33 Combine like terms: 33 + -33 = 0 0 + 7t = -52 + -33 7t = -52 + -33 Combine like terms: -52 + -33 = -85 7t = -85 Divide each side by '7'. t = -12.14285714 Simplifying t = -12.14285714
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