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Simplifying 0.05(z + -7) + -0.09 + 0.03z = 3.97 + -0.01z Reorder the terms: 0.05(-7 + z) + -0.09 + 0.03z = 3.97 + -0.01z (-7 * 0.05 + z * 0.05) + -0.09 + 0.03z = 3.97 + -0.01z (-0.35 + 0.05z) + -0.09 + 0.03z = 3.97 + -0.01z Reorder the terms: -0.35 + -0.09 + 0.05z + 0.03z = 3.97 + -0.01z Combine like terms: -0.35 + -0.09 = -0.44 -0.44 + 0.05z + 0.03z = 3.97 + -0.01z Combine like terms: 0.05z + 0.03z = 0.08z -0.44 + 0.08z = 3.97 + -0.01z Solving -0.44 + 0.08z = 3.97 + -0.01z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.01z' to each side of the equation. -0.44 + 0.08z + 0.01z = 3.97 + -0.01z + 0.01z Combine like terms: 0.08z + 0.01z = 0.09z -0.44 + 0.09z = 3.97 + -0.01z + 0.01z Combine like terms: -0.01z + 0.01z = 0.00 -0.44 + 0.09z = 3.97 + 0.00 -0.44 + 0.09z = 3.97 Add '0.44' to each side of the equation. -0.44 + 0.44 + 0.09z = 3.97 + 0.44 Combine like terms: -0.44 + 0.44 = 0.00 0.00 + 0.09z = 3.97 + 0.44 0.09z = 3.97 + 0.44 Combine like terms: 3.97 + 0.44 = 4.41 0.09z = 4.41 Divide each side by '0.09'. z = 49 Simplifying z = 49
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