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Simplifying 6(4z + -1) + -5(z + 4) = 15(z + 1) Reorder the terms: 6(-1 + 4z) + -5(z + 4) = 15(z + 1) (-1 * 6 + 4z * 6) + -5(z + 4) = 15(z + 1) (-6 + 24z) + -5(z + 4) = 15(z + 1) Reorder the terms: -6 + 24z + -5(4 + z) = 15(z + 1) -6 + 24z + (4 * -5 + z * -5) = 15(z + 1) -6 + 24z + (-20 + -5z) = 15(z + 1) Reorder the terms: -6 + -20 + 24z + -5z = 15(z + 1) Combine like terms: -6 + -20 = -26 -26 + 24z + -5z = 15(z + 1) Combine like terms: 24z + -5z = 19z -26 + 19z = 15(z + 1) Reorder the terms: -26 + 19z = 15(1 + z) -26 + 19z = (1 * 15 + z * 15) -26 + 19z = (15 + 15z) Solving -26 + 19z = 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. -26 + 19z + -15z = 15 + 15z + -15z Combine like terms: 19z + -15z = 4z -26 + 4z = 15 + 15z + -15z Combine like terms: 15z + -15z = 0 -26 + 4z = 15 + 0 -26 + 4z = 15 Add '26' to each side of the equation. -26 + 26 + 4z = 15 + 26 Combine like terms: -26 + 26 = 0 0 + 4z = 15 + 26 4z = 15 + 26 Combine like terms: 15 + 26 = 41 4z = 41 Divide each side by '4'. z = 10.25 Simplifying z = 10.25
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