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Simplifying -6(t + 4) + 8(-2t + -7) = -23(t + 3) + -9 Reorder the terms: -6(4 + t) + 8(-2t + -7) = -23(t + 3) + -9 (4 * -6 + t * -6) + 8(-2t + -7) = -23(t + 3) + -9 (-24 + -6t) + 8(-2t + -7) = -23(t + 3) + -9 Reorder the terms: -24 + -6t + 8(-7 + -2t) = -23(t + 3) + -9 -24 + -6t + (-7 * 8 + -2t * 8) = -23(t + 3) + -9 -24 + -6t + (-56 + -16t) = -23(t + 3) + -9 Reorder the terms: -24 + -56 + -6t + -16t = -23(t + 3) + -9 Combine like terms: -24 + -56 = -80 -80 + -6t + -16t = -23(t + 3) + -9 Combine like terms: -6t + -16t = -22t -80 + -22t = -23(t + 3) + -9 Reorder the terms: -80 + -22t = -23(3 + t) + -9 -80 + -22t = (3 * -23 + t * -23) + -9 -80 + -22t = (-69 + -23t) + -9 Reorder the terms: -80 + -22t = -69 + -9 + -23t Combine like terms: -69 + -9 = -78 -80 + -22t = -78 + -23t Solving -80 + -22t = -78 + -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. -80 + -22t + 23t = -78 + -23t + 23t Combine like terms: -22t + 23t = 1t -80 + 1t = -78 + -23t + 23t Combine like terms: -23t + 23t = 0 -80 + 1t = -78 + 0 -80 + 1t = -78 Add '80' to each side of the equation. -80 + 80 + 1t = -78 + 80 Combine like terms: -80 + 80 = 0 0 + 1t = -78 + 80 1t = -78 + 80 Combine like terms: -78 + 80 = 2 1t = 2 Divide each side by '1'. t = 2 Simplifying t = 2
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