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Simplifying 0.5(z + -6) + -0.4(z + -5) + 0.3(z + -4) = 0 Reorder the terms: 0.5(-6 + z) + -0.4(z + -5) + 0.3(z + -4) = 0 (-6 * 0.5 + z * 0.5) + -0.4(z + -5) + 0.3(z + -4) = 0 (-3 + 0.5z) + -0.4(z + -5) + 0.3(z + -4) = 0 Reorder the terms: -3 + 0.5z + -0.4(-5 + z) + 0.3(z + -4) = 0 -3 + 0.5z + (-5 * -0.4 + z * -0.4) + 0.3(z + -4) = 0 -3 + 0.5z + (2 + -0.4z) + 0.3(z + -4) = 0 Reorder the terms: -3 + 0.5z + 2 + -0.4z + 0.3(-4 + z) = 0 -3 + 0.5z + 2 + -0.4z + (-4 * 0.3 + z * 0.3) = 0 -3 + 0.5z + 2 + -0.4z + (-1.2 + 0.3z) = 0 Reorder the terms: -3 + 2 + -1.2 + 0.5z + -0.4z + 0.3z = 0 Combine like terms: -3 + 2 = -1 -1 + -1.2 + 0.5z + -0.4z + 0.3z = 0 Combine like terms: -1 + -1.2 = -2.2 -2.2 + 0.5z + -0.4z + 0.3z = 0 Combine like terms: 0.5z + -0.4z = 0.1z -2.2 + 0.1z + 0.3z = 0 Combine like terms: 0.1z + 0.3z = 0.4z -2.2 + 0.4z = 0 Solving -2.2 + 0.4z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + 0.4z = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 0.4z = 0 + 2.2 0.4z = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 0.4z = 2.2 Divide each side by '0.4'. z = 5.5 Simplifying z = 5.5
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