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Simplifying 0.4(z + 1) + -0.7z = -0.1 + 0.7 + -0.2z + -0.3 Reorder the terms: 0.4(1 + z) + -0.7z = -0.1 + 0.7 + -0.2z + -0.3 (1 * 0.4 + z * 0.4) + -0.7z = -0.1 + 0.7 + -0.2z + -0.3 (0.4 + 0.4z) + -0.7z = -0.1 + 0.7 + -0.2z + -0.3 Combine like terms: 0.4z + -0.7z = -0.3z 0.4 + -0.3z = -0.1 + 0.7 + -0.2z + -0.3 Reorder the terms: 0.4 + -0.3z = -0.1 + 0.7 + -0.3 + -0.2z Combine like terms: -0.1 + 0.7 = 0.6 0.4 + -0.3z = 0.6 + -0.3 + -0.2z Combine like terms: 0.6 + -0.3 = 0.3 0.4 + -0.3z = 0.3 + -0.2z Solving 0.4 + -0.3z = 0.3 + -0.2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.2z' to each side of the equation. 0.4 + -0.3z + 0.2z = 0.3 + -0.2z + 0.2z Combine like terms: -0.3z + 0.2z = -0.1z 0.4 + -0.1z = 0.3 + -0.2z + 0.2z Combine like terms: -0.2z + 0.2z = 0.0 0.4 + -0.1z = 0.3 + 0.0 0.4 + -0.1z = 0.3 Add '-0.4' to each side of the equation. 0.4 + -0.4 + -0.1z = 0.3 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.1z = 0.3 + -0.4 -0.1z = 0.3 + -0.4 Combine like terms: 0.3 + -0.4 = -0.1 -0.1z = -0.1 Divide each side by '-0.1'. z = 1 Simplifying z = 1
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