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Simplifying 9(30 + -12t) = 8(6 + 9t) + -24t (30 * 9 + -12t * 9) = 8(6 + 9t) + -24t (270 + -108t) = 8(6 + 9t) + -24t 270 + -108t = (6 * 8 + 9t * 8) + -24t 270 + -108t = (48 + 72t) + -24t Combine like terms: 72t + -24t = 48t 270 + -108t = 48 + 48t Solving 270 + -108t = 48 + 48t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-48t' to each side of the equation. 270 + -108t + -48t = 48 + 48t + -48t Combine like terms: -108t + -48t = -156t 270 + -156t = 48 + 48t + -48t Combine like terms: 48t + -48t = 0 270 + -156t = 48 + 0 270 + -156t = 48 Add '-270' to each side of the equation. 270 + -270 + -156t = 48 + -270 Combine like terms: 270 + -270 = 0 0 + -156t = 48 + -270 -156t = 48 + -270 Combine like terms: 48 + -270 = -222 -156t = -222 Divide each side by '-156'. t = 1.423076923 Simplifying t = 1.423076923
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