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Simplifying -7(t + 3) + 3(-5t + -8) = -23(t + 1) + 3 Reorder the terms: -7(3 + t) + 3(-5t + -8) = -23(t + 1) + 3 (3 * -7 + t * -7) + 3(-5t + -8) = -23(t + 1) + 3 (-21 + -7t) + 3(-5t + -8) = -23(t + 1) + 3 Reorder the terms: -21 + -7t + 3(-8 + -5t) = -23(t + 1) + 3 -21 + -7t + (-8 * 3 + -5t * 3) = -23(t + 1) + 3 -21 + -7t + (-24 + -15t) = -23(t + 1) + 3 Reorder the terms: -21 + -24 + -7t + -15t = -23(t + 1) + 3 Combine like terms: -21 + -24 = -45 -45 + -7t + -15t = -23(t + 1) + 3 Combine like terms: -7t + -15t = -22t -45 + -22t = -23(t + 1) + 3 Reorder the terms: -45 + -22t = -23(1 + t) + 3 -45 + -22t = (1 * -23 + t * -23) + 3 -45 + -22t = (-23 + -23t) + 3 Reorder the terms: -45 + -22t = -23 + 3 + -23t Combine like terms: -23 + 3 = -20 -45 + -22t = -20 + -23t Solving -45 + -22t = -20 + -23t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '23t' to each side of the equation. -45 + -22t + 23t = -20 + -23t + 23t Combine like terms: -22t + 23t = 1t -45 + 1t = -20 + -23t + 23t Combine like terms: -23t + 23t = 0 -45 + 1t = -20 + 0 -45 + 1t = -20 Add '45' to each side of the equation. -45 + 45 + 1t = -20 + 45 Combine like terms: -45 + 45 = 0 0 + 1t = -20 + 45 1t = -20 + 45 Combine like terms: -20 + 45 = 25 1t = 25 Divide each side by '1'. t = 25 Simplifying t = 25
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