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Simplifying 0.3(3z + 6) + 5.2 = 0.4(3z + -5) Reorder the terms: 0.3(6 + 3z) + 5.2 = 0.4(3z + -5) (6 * 0.3 + 3z * 0.3) + 5.2 = 0.4(3z + -5) (1.8 + 0.9z) + 5.2 = 0.4(3z + -5) Reorder the terms: 1.8 + 5.2 + 0.9z = 0.4(3z + -5) Combine like terms: 1.8 + 5.2 = 7 7 + 0.9z = 0.4(3z + -5) Reorder the terms: 7 + 0.9z = 0.4(-5 + 3z) 7 + 0.9z = (-5 * 0.4 + 3z * 0.4) 7 + 0.9z = (-2 + 1.2z) Solving 7 + 0.9z = -2 + 1.2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.2z' to each side of the equation. 7 + 0.9z + -1.2z = -2 + 1.2z + -1.2z Combine like terms: 0.9z + -1.2z = -0.3z 7 + -0.3z = -2 + 1.2z + -1.2z Combine like terms: 1.2z + -1.2z = 0.0 7 + -0.3z = -2 + 0.0 7 + -0.3z = -2 Add '-7' to each side of the equation. 7 + -7 + -0.3z = -2 + -7 Combine like terms: 7 + -7 = 0 0 + -0.3z = -2 + -7 -0.3z = -2 + -7 Combine like terms: -2 + -7 = -9 -0.3z = -9 Divide each side by '-0.3'. z = 30 Simplifying z = 30
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