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Simplifying 6(t + 5) + 6(-8t + -9) = -43(t + 1) + -10 Reorder the terms: 6(5 + t) + 6(-8t + -9) = -43(t + 1) + -10 (5 * 6 + t * 6) + 6(-8t + -9) = -43(t + 1) + -10 (30 + 6t) + 6(-8t + -9) = -43(t + 1) + -10 Reorder the terms: 30 + 6t + 6(-9 + -8t) = -43(t + 1) + -10 30 + 6t + (-9 * 6 + -8t * 6) = -43(t + 1) + -10 30 + 6t + (-54 + -48t) = -43(t + 1) + -10 Reorder the terms: 30 + -54 + 6t + -48t = -43(t + 1) + -10 Combine like terms: 30 + -54 = -24 -24 + 6t + -48t = -43(t + 1) + -10 Combine like terms: 6t + -48t = -42t -24 + -42t = -43(t + 1) + -10 Reorder the terms: -24 + -42t = -43(1 + t) + -10 -24 + -42t = (1 * -43 + t * -43) + -10 -24 + -42t = (-43 + -43t) + -10 Reorder the terms: -24 + -42t = -43 + -10 + -43t Combine like terms: -43 + -10 = -53 -24 + -42t = -53 + -43t Solving -24 + -42t = -53 + -43t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '43t' to each side of the equation. -24 + -42t + 43t = -53 + -43t + 43t Combine like terms: -42t + 43t = 1t -24 + 1t = -53 + -43t + 43t Combine like terms: -43t + 43t = 0 -24 + 1t = -53 + 0 -24 + 1t = -53 Add '24' to each side of the equation. -24 + 24 + 1t = -53 + 24 Combine like terms: -24 + 24 = 0 0 + 1t = -53 + 24 1t = -53 + 24 Combine like terms: -53 + 24 = -29 1t = -29 Divide each side by '1'. t = -29 Simplifying t = -29
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