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Simplifying 0.4(3z + 6) + 21.8 = 0.7(3z + -4) Reorder the terms: 0.4(6 + 3z) + 21.8 = 0.7(3z + -4) (6 * 0.4 + 3z * 0.4) + 21.8 = 0.7(3z + -4) (2.4 + 1.2z) + 21.8 = 0.7(3z + -4) Reorder the terms: 2.4 + 21.8 + 1.2z = 0.7(3z + -4) Combine like terms: 2.4 + 21.8 = 24.2 24.2 + 1.2z = 0.7(3z + -4) Reorder the terms: 24.2 + 1.2z = 0.7(-4 + 3z) 24.2 + 1.2z = (-4 * 0.7 + 3z * 0.7) 24.2 + 1.2z = (-2.8 + 2.1z) Solving 24.2 + 1.2z = -2.8 + 2.1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.1z' to each side of the equation. 24.2 + 1.2z + -2.1z = -2.8 + 2.1z + -2.1z Combine like terms: 1.2z + -2.1z = -0.9z 24.2 + -0.9z = -2.8 + 2.1z + -2.1z Combine like terms: 2.1z + -2.1z = 0.0 24.2 + -0.9z = -2.8 + 0.0 24.2 + -0.9z = -2.8 Add '-24.2' to each side of the equation. 24.2 + -24.2 + -0.9z = -2.8 + -24.2 Combine like terms: 24.2 + -24.2 = 0.0 0.0 + -0.9z = -2.8 + -24.2 -0.9z = -2.8 + -24.2 Combine like terms: -2.8 + -24.2 = -27 -0.9z = -27 Divide each side by '-0.9'. z = 30 Simplifying z = 30
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