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Simplifying 6(4z + -1) + -2(z + 4) = 15(z + 1) Reorder the terms: 6(-1 + 4z) + -2(z + 4) = 15(z + 1) (-1 * 6 + 4z * 6) + -2(z + 4) = 15(z + 1) (-6 + 24z) + -2(z + 4) = 15(z + 1) Reorder the terms: -6 + 24z + -2(4 + z) = 15(z + 1) -6 + 24z + (4 * -2 + z * -2) = 15(z + 1) -6 + 24z + (-8 + -2z) = 15(z + 1) Reorder the terms: -6 + -8 + 24z + -2z = 15(z + 1) Combine like terms: -6 + -8 = -14 -14 + 24z + -2z = 15(z + 1) Combine like terms: 24z + -2z = 22z -14 + 22z = 15(z + 1) Reorder the terms: -14 + 22z = 15(1 + z) -14 + 22z = (1 * 15 + z * 15) -14 + 22z = (15 + 15z) Solving -14 + 22z = 15 + 15z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15z' to each side of the equation. -14 + 22z + -15z = 15 + 15z + -15z Combine like terms: 22z + -15z = 7z -14 + 7z = 15 + 15z + -15z Combine like terms: 15z + -15z = 0 -14 + 7z = 15 + 0 -14 + 7z = 15 Add '14' to each side of the equation. -14 + 14 + 7z = 15 + 14 Combine like terms: -14 + 14 = 0 0 + 7z = 15 + 14 7z = 15 + 14 Combine like terms: 15 + 14 = 29 7z = 29 Divide each side by '7'. z = 4.142857143 Simplifying z = 4.142857143
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