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Simplifying 8(t + -6) + 5(-3t + -2) = -8(t + 7) + -5 Reorder the terms: 8(-6 + t) + 5(-3t + -2) = -8(t + 7) + -5 (-6 * 8 + t * 8) + 5(-3t + -2) = -8(t + 7) + -5 (-48 + 8t) + 5(-3t + -2) = -8(t + 7) + -5 Reorder the terms: -48 + 8t + 5(-2 + -3t) = -8(t + 7) + -5 -48 + 8t + (-2 * 5 + -3t * 5) = -8(t + 7) + -5 -48 + 8t + (-10 + -15t) = -8(t + 7) + -5 Reorder the terms: -48 + -10 + 8t + -15t = -8(t + 7) + -5 Combine like terms: -48 + -10 = -58 -58 + 8t + -15t = -8(t + 7) + -5 Combine like terms: 8t + -15t = -7t -58 + -7t = -8(t + 7) + -5 Reorder the terms: -58 + -7t = -8(7 + t) + -5 -58 + -7t = (7 * -8 + t * -8) + -5 -58 + -7t = (-56 + -8t) + -5 Reorder the terms: -58 + -7t = -56 + -5 + -8t Combine like terms: -56 + -5 = -61 -58 + -7t = -61 + -8t Solving -58 + -7t = -61 + -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. -58 + -7t + 8t = -61 + -8t + 8t Combine like terms: -7t + 8t = 1t -58 + 1t = -61 + -8t + 8t Combine like terms: -8t + 8t = 0 -58 + 1t = -61 + 0 -58 + 1t = -61 Add '58' to each side of the equation. -58 + 58 + 1t = -61 + 58 Combine like terms: -58 + 58 = 0 0 + 1t = -61 + 58 1t = -61 + 58 Combine like terms: -61 + 58 = -3 1t = -3 Divide each side by '1'. t = -3 Simplifying t = -3
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