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Simplifying 0.005(7t + -3) = 0.35(t + -1) + 0.2 Reorder the terms: 0.005(-3 + 7t) = 0.35(t + -1) + 0.2 (-3 * 0.005 + 7t * 0.005) = 0.35(t + -1) + 0.2 (-0.015 + 0.035t) = 0.35(t + -1) + 0.2 Reorder the terms: -0.015 + 0.035t = 0.35(-1 + t) + 0.2 -0.015 + 0.035t = (-1 * 0.35 + t * 0.35) + 0.2 -0.015 + 0.035t = (-0.35 + 0.35t) + 0.2 Reorder the terms: -0.015 + 0.035t = -0.35 + 0.2 + 0.35t Combine like terms: -0.35 + 0.2 = -0.15 -0.015 + 0.035t = -0.15 + 0.35t Solving -0.015 + 0.035t = -0.15 + 0.35t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.35t' to each side of the equation. -0.015 + 0.035t + -0.35t = -0.15 + 0.35t + -0.35t Combine like terms: 0.035t + -0.35t = -0.315t -0.015 + -0.315t = -0.15 + 0.35t + -0.35t Combine like terms: 0.35t + -0.35t = 0.00 -0.015 + -0.315t = -0.15 + 0.00 -0.015 + -0.315t = -0.15 Add '0.015' to each side of the equation. -0.015 + 0.015 + -0.315t = -0.15 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + -0.315t = -0.15 + 0.015 -0.315t = -0.15 + 0.015 Combine like terms: -0.15 + 0.015 = -0.135 -0.315t = -0.135 Divide each side by '-0.315'. t = 0.4285714286 Simplifying t = 0.4285714286
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