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Simplifying 0.4(4z + 7) + 10.7 = 0.5(4z + -5) Reorder the terms: 0.4(7 + 4z) + 10.7 = 0.5(4z + -5) (7 * 0.4 + 4z * 0.4) + 10.7 = 0.5(4z + -5) (2.8 + 1.6z) + 10.7 = 0.5(4z + -5) Reorder the terms: 2.8 + 10.7 + 1.6z = 0.5(4z + -5) Combine like terms: 2.8 + 10.7 = 13.5 13.5 + 1.6z = 0.5(4z + -5) Reorder the terms: 13.5 + 1.6z = 0.5(-5 + 4z) 13.5 + 1.6z = (-5 * 0.5 + 4z * 0.5) 13.5 + 1.6z = (-2.5 + 2z) Solving 13.5 + 1.6z = -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. 13.5 + 1.6z + -2z = -2.5 + 2z + -2z Combine like terms: 1.6z + -2z = -0.4z 13.5 + -0.4z = -2.5 + 2z + -2z Combine like terms: 2z + -2z = 0 13.5 + -0.4z = -2.5 + 0 13.5 + -0.4z = -2.5 Add '-13.5' to each side of the equation. 13.5 + -13.5 + -0.4z = -2.5 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -0.4z = -2.5 + -13.5 -0.4z = -2.5 + -13.5 Combine like terms: -2.5 + -13.5 = -16 -0.4z = -16 Divide each side by '-0.4'. z = 40 Simplifying z = 40
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