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Simplifying 0.06(3t + -7) = 0.10(t + -5) + 0.48 Reorder the terms: 0.06(-7 + 3t) = 0.10(t + -5) + 0.48 (-7 * 0.06 + 3t * 0.06) = 0.10(t + -5) + 0.48 (-0.42 + 0.18t) = 0.10(t + -5) + 0.48 Reorder the terms: -0.42 + 0.18t = 0.10(-5 + t) + 0.48 -0.42 + 0.18t = (-5 * 0.10 + t * 0.10) + 0.48 -0.42 + 0.18t = (-0.5 + 0.10t) + 0.48 Reorder the terms: -0.42 + 0.18t = -0.5 + 0.48 + 0.10t Combine like terms: -0.5 + 0.48 = -0.02 -0.42 + 0.18t = -0.02 + 0.10t Solving -0.42 + 0.18t = -0.02 + 0.10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.10t' to each side of the equation. -0.42 + 0.18t + -0.10t = -0.02 + 0.10t + -0.10t Combine like terms: 0.18t + -0.10t = 0.08t -0.42 + 0.08t = -0.02 + 0.10t + -0.10t Combine like terms: 0.10t + -0.10t = 0.00 -0.42 + 0.08t = -0.02 + 0.00 -0.42 + 0.08t = -0.02 Add '0.42' to each side of the equation. -0.42 + 0.42 + 0.08t = -0.02 + 0.42 Combine like terms: -0.42 + 0.42 = 0.00 0.00 + 0.08t = -0.02 + 0.42 0.08t = -0.02 + 0.42 Combine like terms: -0.02 + 0.42 = 0.4 0.08t = 0.4 Divide each side by '0.08'. t = 5 Simplifying t = 5
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