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Simplifying 6(4z + -1) + -5(z + 4) = 11(z + 1) Reorder the terms: 6(-1 + 4z) + -5(z + 4) = 11(z + 1) (-1 * 6 + 4z * 6) + -5(z + 4) = 11(z + 1) (-6 + 24z) + -5(z + 4) = 11(z + 1) Reorder the terms: -6 + 24z + -5(4 + z) = 11(z + 1) -6 + 24z + (4 * -5 + z * -5) = 11(z + 1) -6 + 24z + (-20 + -5z) = 11(z + 1) Reorder the terms: -6 + -20 + 24z + -5z = 11(z + 1) Combine like terms: -6 + -20 = -26 -26 + 24z + -5z = 11(z + 1) Combine like terms: 24z + -5z = 19z -26 + 19z = 11(z + 1) Reorder the terms: -26 + 19z = 11(1 + z) -26 + 19z = (1 * 11 + z * 11) -26 + 19z = (11 + 11z) Solving -26 + 19z = 11 + 11z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11z' to each side of the equation. -26 + 19z + -11z = 11 + 11z + -11z Combine like terms: 19z + -11z = 8z -26 + 8z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -26 + 8z = 11 + 0 -26 + 8z = 11 Add '26' to each side of the equation. -26 + 26 + 8z = 11 + 26 Combine like terms: -26 + 26 = 0 0 + 8z = 11 + 26 8z = 11 + 26 Combine like terms: 11 + 26 = 37 8z = 37 Divide each side by '8'. z = 4.625 Simplifying z = 4.625
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