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Simplifying 4(0.125t + 2) = 2(t + -8) + -0.5t Reorder the terms: 4(2 + 0.125t) = 2(t + -8) + -0.5t (2 * 4 + 0.125t * 4) = 2(t + -8) + -0.5t (8 + 0.5t) = 2(t + -8) + -0.5t Reorder the terms: 8 + 0.5t = 2(-8 + t) + -0.5t 8 + 0.5t = (-8 * 2 + t * 2) + -0.5t 8 + 0.5t = (-16 + 2t) + -0.5t Combine like terms: 2t + -0.5t = 1.5t 8 + 0.5t = -16 + 1.5t Solving 8 + 0.5t = -16 + 1.5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5t' to each side of the equation. 8 + 0.5t + -1.5t = -16 + 1.5t + -1.5t Combine like terms: 0.5t + -1.5t = -1t 8 + -1t = -16 + 1.5t + -1.5t Combine like terms: 1.5t + -1.5t = 0.0 8 + -1t = -16 + 0.0 8 + -1t = -16 Add '-8' to each side of the equation. 8 + -8 + -1t = -16 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = -16 + -8 -1t = -16 + -8 Combine like terms: -16 + -8 = -24 -1t = -24 Divide each side by '-1'. t = 24 Simplifying t = 24
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