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Simplifying 1.4(z + -5) + -0.2 = 0.5(6z + 4) Reorder the terms: 1.4(-5 + z) + -0.2 = 0.5(6z + 4) (-5 * 1.4 + z * 1.4) + -0.2 = 0.5(6z + 4) (-7 + 1.4z) + -0.2 = 0.5(6z + 4) Reorder the terms: -7 + -0.2 + 1.4z = 0.5(6z + 4) Combine like terms: -7 + -0.2 = -7.2 -7.2 + 1.4z = 0.5(6z + 4) Reorder the terms: -7.2 + 1.4z = 0.5(4 + 6z) -7.2 + 1.4z = (4 * 0.5 + 6z * 0.5) -7.2 + 1.4z = (2 + 3z) Solving -7.2 + 1.4z = 2 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -7.2 + 1.4z + -3z = 2 + 3z + -3z Combine like terms: 1.4z + -3z = -1.6z -7.2 + -1.6z = 2 + 3z + -3z Combine like terms: 3z + -3z = 0 -7.2 + -1.6z = 2 + 0 -7.2 + -1.6z = 2 Add '7.2' to each side of the equation. -7.2 + 7.2 + -1.6z = 2 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -1.6z = 2 + 7.2 -1.6z = 2 + 7.2 Combine like terms: 2 + 7.2 = 9.2 -1.6z = 9.2 Divide each side by '-1.6'. z = -5.75 Simplifying z = -5.75
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