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Simplifying 7 + 6(-5z + 3) = -3(8z + 6) + 8 Reorder the terms: 7 + 6(3 + -5z) = -3(8z + 6) + 8 7 + (3 * 6 + -5z * 6) = -3(8z + 6) + 8 7 + (18 + -30z) = -3(8z + 6) + 8 Combine like terms: 7 + 18 = 25 25 + -30z = -3(8z + 6) + 8 Reorder the terms: 25 + -30z = -3(6 + 8z) + 8 25 + -30z = (6 * -3 + 8z * -3) + 8 25 + -30z = (-18 + -24z) + 8 Reorder the terms: 25 + -30z = -18 + 8 + -24z Combine like terms: -18 + 8 = -10 25 + -30z = -10 + -24z Solving 25 + -30z = -10 + -24z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '24z' to each side of the equation. 25 + -30z + 24z = -10 + -24z + 24z Combine like terms: -30z + 24z = -6z 25 + -6z = -10 + -24z + 24z Combine like terms: -24z + 24z = 0 25 + -6z = -10 + 0 25 + -6z = -10 Add '-25' to each side of the equation. 25 + -25 + -6z = -10 + -25 Combine like terms: 25 + -25 = 0 0 + -6z = -10 + -25 -6z = -10 + -25 Combine like terms: -10 + -25 = -35 -6z = -35 Divide each side by '-6'. z = 5.833333333 Simplifying z = 5.833333333
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