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Simplifying 0.4(4z + 5) + 29.8 = 0.7(4z + -6) Reorder the terms: 0.4(5 + 4z) + 29.8 = 0.7(4z + -6) (5 * 0.4 + 4z * 0.4) + 29.8 = 0.7(4z + -6) (2 + 1.6z) + 29.8 = 0.7(4z + -6) Reorder the terms: 2 + 29.8 + 1.6z = 0.7(4z + -6) Combine like terms: 2 + 29.8 = 31.8 31.8 + 1.6z = 0.7(4z + -6) Reorder the terms: 31.8 + 1.6z = 0.7(-6 + 4z) 31.8 + 1.6z = (-6 * 0.7 + 4z * 0.7) 31.8 + 1.6z = (-4.2 + 2.8z) Solving 31.8 + 1.6z = -4.2 + 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. 31.8 + 1.6z + -2.8z = -4.2 + 2.8z + -2.8z Combine like terms: 1.6z + -2.8z = -1.2z 31.8 + -1.2z = -4.2 + 2.8z + -2.8z Combine like terms: 2.8z + -2.8z = 0.0 31.8 + -1.2z = -4.2 + 0.0 31.8 + -1.2z = -4.2 Add '-31.8' to each side of the equation. 31.8 + -31.8 + -1.2z = -4.2 + -31.8 Combine like terms: 31.8 + -31.8 = 0.0 0.0 + -1.2z = -4.2 + -31.8 -1.2z = -4.2 + -31.8 Combine like terms: -4.2 + -31.8 = -36 -1.2z = -36 Divide each side by '-1.2'. z = 30 Simplifying z = 30
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