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Simplifying 6.5(1z + -2) = 2.5(3z + 3) + -6.5 Reorder the terms: 6.5(-2 + 1z) = 2.5(3z + 3) + -6.5 (-2 * 6.5 + 1z * 6.5) = 2.5(3z + 3) + -6.5 (-13 + 6.5z) = 2.5(3z + 3) + -6.5 Reorder the terms: -13 + 6.5z = 2.5(3 + 3z) + -6.5 -13 + 6.5z = (3 * 2.5 + 3z * 2.5) + -6.5 -13 + 6.5z = (7.5 + 7.5z) + -6.5 Reorder the terms: -13 + 6.5z = 7.5 + -6.5 + 7.5z Combine like terms: 7.5 + -6.5 = 1 -13 + 6.5z = 1 + 7.5z Solving -13 + 6.5z = 1 + 7.5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7.5z' to each side of the equation. -13 + 6.5z + -7.5z = 1 + 7.5z + -7.5z Combine like terms: 6.5z + -7.5z = -1z -13 + -1z = 1 + 7.5z + -7.5z Combine like terms: 7.5z + -7.5z = 0.0 -13 + -1z = 1 + 0.0 -13 + -1z = 1 Add '13' to each side of the equation. -13 + 13 + -1z = 1 + 13 Combine like terms: -13 + 13 = 0 0 + -1z = 1 + 13 -1z = 1 + 13 Combine like terms: 1 + 13 = 14 -1z = 14 Divide each side by '-1'. z = -14 Simplifying z = -14
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