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Simplifying 0.3(4z + 6) + 27.7 = 0.5(4z + -5) Reorder the terms: 0.3(6 + 4z) + 27.7 = 0.5(4z + -5) (6 * 0.3 + 4z * 0.3) + 27.7 = 0.5(4z + -5) (1.8 + 1.2z) + 27.7 = 0.5(4z + -5) Reorder the terms: 1.8 + 27.7 + 1.2z = 0.5(4z + -5) Combine like terms: 1.8 + 27.7 = 29.5 29.5 + 1.2z = 0.5(4z + -5) Reorder the terms: 29.5 + 1.2z = 0.5(-5 + 4z) 29.5 + 1.2z = (-5 * 0.5 + 4z * 0.5) 29.5 + 1.2z = (-2.5 + 2z) Solving 29.5 + 1.2z = -2.5 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. 29.5 + 1.2z + -2z = -2.5 + 2z + -2z Combine like terms: 1.2z + -2z = -0.8z 29.5 + -0.8z = -2.5 + 2z + -2z Combine like terms: 2z + -2z = 0 29.5 + -0.8z = -2.5 + 0 29.5 + -0.8z = -2.5 Add '-29.5' to each side of the equation. 29.5 + -29.5 + -0.8z = -2.5 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + -0.8z = -2.5 + -29.5 -0.8z = -2.5 + -29.5 Combine like terms: -2.5 + -29.5 = -32 -0.8z = -32 Divide each side by '-0.8'. z = 40 Simplifying z = 40
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