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Simplifying 0.4(4z + 6) + 17.4 = 0.7(4z + -6) Reorder the terms: 0.4(6 + 4z) + 17.4 = 0.7(4z + -6) (6 * 0.4 + 4z * 0.4) + 17.4 = 0.7(4z + -6) (2.4 + 1.6z) + 17.4 = 0.7(4z + -6) Reorder the terms: 2.4 + 17.4 + 1.6z = 0.7(4z + -6) Combine like terms: 2.4 + 17.4 = 19.8 19.8 + 1.6z = 0.7(4z + -6) Reorder the terms: 19.8 + 1.6z = 0.7(-6 + 4z) 19.8 + 1.6z = (-6 * 0.7 + 4z * 0.7) 19.8 + 1.6z = (-4.2 + 2.8z) Solving 19.8 + 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. 19.8 + 1.6z + -2.8z = -4.2 + 2.8z + -2.8z Combine like terms: 1.6z + -2.8z = -1.2z 19.8 + -1.2z = -4.2 + 2.8z + -2.8z Combine like terms: 2.8z + -2.8z = 0.0 19.8 + -1.2z = -4.2 + 0.0 19.8 + -1.2z = -4.2 Add '-19.8' to each side of the equation. 19.8 + -19.8 + -1.2z = -4.2 + -19.8 Combine like terms: 19.8 + -19.8 = 0.0 0.0 + -1.2z = -4.2 + -19.8 -1.2z = -4.2 + -19.8 Combine like terms: -4.2 + -19.8 = -24 -1.2z = -24 Divide each side by '-1.2'. z = 20 Simplifying z = 20
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