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Simplifying 6(5z + -1) + -2(z + 5) = 7(z + 1) Reorder the terms: 6(-1 + 5z) + -2(z + 5) = 7(z + 1) (-1 * 6 + 5z * 6) + -2(z + 5) = 7(z + 1) (-6 + 30z) + -2(z + 5) = 7(z + 1) Reorder the terms: -6 + 30z + -2(5 + z) = 7(z + 1) -6 + 30z + (5 * -2 + z * -2) = 7(z + 1) -6 + 30z + (-10 + -2z) = 7(z + 1) Reorder the terms: -6 + -10 + 30z + -2z = 7(z + 1) Combine like terms: -6 + -10 = -16 -16 + 30z + -2z = 7(z + 1) Combine like terms: 30z + -2z = 28z -16 + 28z = 7(z + 1) Reorder the terms: -16 + 28z = 7(1 + z) -16 + 28z = (1 * 7 + z * 7) -16 + 28z = (7 + 7z) Solving -16 + 28z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -16 + 28z + -7z = 7 + 7z + -7z Combine like terms: 28z + -7z = 21z -16 + 21z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -16 + 21z = 7 + 0 -16 + 21z = 7 Add '16' to each side of the equation. -16 + 16 + 21z = 7 + 16 Combine like terms: -16 + 16 = 0 0 + 21z = 7 + 16 21z = 7 + 16 Combine like terms: 7 + 16 = 23 21z = 23 Divide each side by '21'. z = 1.095238095 Simplifying z = 1.095238095
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