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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 Reorder the terms for easier multiplication: -80 + -22t = -23 * 9(3 + t) Multiply -23 * 9 -80 + -22t = -207(3 + t) -80 + -22t = (3 * -207 + t * -207) -80 + -22t = (-621 + -207t) Solving -80 + -22t = -621 + -207t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '207t' to each side of the equation. -80 + -22t + 207t = -621 + -207t + 207t Combine like terms: -22t + 207t = 185t -80 + 185t = -621 + -207t + 207t Combine like terms: -207t + 207t = 0 -80 + 185t = -621 + 0 -80 + 185t = -621 Add '80' to each side of the equation. -80 + 80 + 185t = -621 + 80 Combine like terms: -80 + 80 = 0 0 + 185t = -621 + 80 185t = -621 + 80 Combine like terms: -621 + 80 = -541 185t = -541 Divide each side by '185'. t = -2.924324324 Simplifying t = -2.924324324
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