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Simplifying 0.04(3t + 4) = 0.09(t + -4) + 0.48 Reorder the terms: 0.04(4 + 3t) = 0.09(t + -4) + 0.48 (4 * 0.04 + 3t * 0.04) = 0.09(t + -4) + 0.48 (0.16 + 0.12t) = 0.09(t + -4) + 0.48 Reorder the terms: 0.16 + 0.12t = 0.09(-4 + t) + 0.48 0.16 + 0.12t = (-4 * 0.09 + t * 0.09) + 0.48 0.16 + 0.12t = (-0.36 + 0.09t) + 0.48 Reorder the terms: 0.16 + 0.12t = -0.36 + 0.48 + 0.09t Combine like terms: -0.36 + 0.48 = 0.12 0.16 + 0.12t = 0.12 + 0.09t Solving 0.16 + 0.12t = 0.12 + 0.09t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.09t' to each side of the equation. 0.16 + 0.12t + -0.09t = 0.12 + 0.09t + -0.09t Combine like terms: 0.12t + -0.09t = 0.03t 0.16 + 0.03t = 0.12 + 0.09t + -0.09t Combine like terms: 0.09t + -0.09t = 0.00 0.16 + 0.03t = 0.12 + 0.00 0.16 + 0.03t = 0.12 Add '-0.16' to each side of the equation. 0.16 + -0.16 + 0.03t = 0.12 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + 0.03t = 0.12 + -0.16 0.03t = 0.12 + -0.16 Combine like terms: 0.12 + -0.16 = -0.04 0.03t = -0.04 Divide each side by '0.03'. t = -1.333333333 Simplifying t = -1.333333333
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