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Simplifying 0.4(3z + 6) + 4.6 = 0.5(3z + -4) Reorder the terms: 0.4(6 + 3z) + 4.6 = 0.5(3z + -4) (6 * 0.4 + 3z * 0.4) + 4.6 = 0.5(3z + -4) (2.4 + 1.2z) + 4.6 = 0.5(3z + -4) Reorder the terms: 2.4 + 4.6 + 1.2z = 0.5(3z + -4) Combine like terms: 2.4 + 4.6 = 7 7 + 1.2z = 0.5(3z + -4) Reorder the terms: 7 + 1.2z = 0.5(-4 + 3z) 7 + 1.2z = (-4 * 0.5 + 3z * 0.5) 7 + 1.2z = (-2 + 1.5z) Solving 7 + 1.2z = -2 + 1.5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.5z' to each side of the equation. 7 + 1.2z + -1.5z = -2 + 1.5z + -1.5z Combine like terms: 1.2z + -1.5z = -0.3z 7 + -0.3z = -2 + 1.5z + -1.5z Combine like terms: 1.5z + -1.5z = 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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