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Simplifying 0.3(3z + -6) + -5.6 = 0.5(3z + -4) Reorder the terms: 0.3(-6 + 3z) + -5.6 = 0.5(3z + -4) (-6 * 0.3 + 3z * 0.3) + -5.6 = 0.5(3z + -4) (-1.8 + 0.9z) + -5.6 = 0.5(3z + -4) Reorder the terms: -1.8 + -5.6 + 0.9z = 0.5(3z + -4) Combine like terms: -1.8 + -5.6 = -7.4 -7.4 + 0.9z = 0.5(3z + -4) Reorder the terms: -7.4 + 0.9z = 0.5(-4 + 3z) -7.4 + 0.9z = (-4 * 0.5 + 3z * 0.5) -7.4 + 0.9z = (-2 + 1.5z) Solving -7.4 + 0.9z = -2 + 1.5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.5z' to each side of the equation. -7.4 + 0.9z + -1.5z = -2 + 1.5z + -1.5z Combine like terms: 0.9z + -1.5z = -0.6z -7.4 + -0.6z = -2 + 1.5z + -1.5z Combine like terms: 1.5z + -1.5z = 0.0 -7.4 + -0.6z = -2 + 0.0 -7.4 + -0.6z = -2 Add '7.4' to each side of the equation. -7.4 + 7.4 + -0.6z = -2 + 7.4 Combine like terms: -7.4 + 7.4 = 0.0 0.0 + -0.6z = -2 + 7.4 -0.6z = -2 + 7.4 Combine like terms: -2 + 7.4 = 5.4 -0.6z = 5.4 Divide each side by '-0.6'. z = -9 Simplifying z = -9
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