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Simplifying 0.5(4z + 7) + 6.1 = 0.6(4z + -4) Reorder the terms: 0.5(7 + 4z) + 6.1 = 0.6(4z + -4) (7 * 0.5 + 4z * 0.5) + 6.1 = 0.6(4z + -4) (3.5 + 2z) + 6.1 = 0.6(4z + -4) Reorder the terms: 3.5 + 6.1 + 2z = 0.6(4z + -4) Combine like terms: 3.5 + 6.1 = 9.6 9.6 + 2z = 0.6(4z + -4) Reorder the terms: 9.6 + 2z = 0.6(-4 + 4z) 9.6 + 2z = (-4 * 0.6 + 4z * 0.6) 9.6 + 2z = (-2.4 + 2.4z) Solving 9.6 + 2z = -2.4 + 2.4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.4z' to each side of the equation. 9.6 + 2z + -2.4z = -2.4 + 2.4z + -2.4z Combine like terms: 2z + -2.4z = -0.4z 9.6 + -0.4z = -2.4 + 2.4z + -2.4z Combine like terms: 2.4z + -2.4z = 0.0 9.6 + -0.4z = -2.4 + 0.0 9.6 + -0.4z = -2.4 Add '-9.6' to each side of the equation. 9.6 + -9.6 + -0.4z = -2.4 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + -0.4z = -2.4 + -9.6 -0.4z = -2.4 + -9.6 Combine like terms: -2.4 + -9.6 = -12 -0.4z = -12 Divide each side by '-0.4'. z = 30 Simplifying z = 30
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