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Simplifying 0.5(4z + 6) + 9.5 = 0.7(4z + -5) Reorder the terms: 0.5(6 + 4z) + 9.5 = 0.7(4z + -5) (6 * 0.5 + 4z * 0.5) + 9.5 = 0.7(4z + -5) (3 + 2z) + 9.5 = 0.7(4z + -5) Reorder the terms: 3 + 9.5 + 2z = 0.7(4z + -5) Combine like terms: 3 + 9.5 = 12.5 12.5 + 2z = 0.7(4z + -5) Reorder the terms: 12.5 + 2z = 0.7(-5 + 4z) 12.5 + 2z = (-5 * 0.7 + 4z * 0.7) 12.5 + 2z = (-3.5 + 2.8z) Solving 12.5 + 2z = -3.5 + 2.8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.8z' to each side of the equation. 12.5 + 2z + -2.8z = -3.5 + 2.8z + -2.8z Combine like terms: 2z + -2.8z = -0.8z 12.5 + -0.8z = -3.5 + 2.8z + -2.8z Combine like terms: 2.8z + -2.8z = 0.0 12.5 + -0.8z = -3.5 + 0.0 12.5 + -0.8z = -3.5 Add '-12.5' to each side of the equation. 12.5 + -12.5 + -0.8z = -3.5 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -0.8z = -3.5 + -12.5 -0.8z = -3.5 + -12.5 Combine like terms: -3.5 + -12.5 = -16 -0.8z = -16 Divide each side by '-0.8'. z = 20 Simplifying z = 20
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