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Simplifying 4(6z + -1) + -5(z + 4) = 11(z + 1) Reorder the terms: 4(-1 + 6z) + -5(z + 4) = 11(z + 1) (-1 * 4 + 6z * 4) + -5(z + 4) = 11(z + 1) (-4 + 24z) + -5(z + 4) = 11(z + 1) Reorder the terms: -4 + 24z + -5(4 + z) = 11(z + 1) -4 + 24z + (4 * -5 + z * -5) = 11(z + 1) -4 + 24z + (-20 + -5z) = 11(z + 1) Reorder the terms: -4 + -20 + 24z + -5z = 11(z + 1) Combine like terms: -4 + -20 = -24 -24 + 24z + -5z = 11(z + 1) Combine like terms: 24z + -5z = 19z -24 + 19z = 11(z + 1) Reorder the terms: -24 + 19z = 11(1 + z) -24 + 19z = (1 * 11 + z * 11) -24 + 19z = (11 + 11z) Solving -24 + 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. -24 + 19z + -11z = 11 + 11z + -11z Combine like terms: 19z + -11z = 8z -24 + 8z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -24 + 8z = 11 + 0 -24 + 8z = 11 Add '24' to each side of the equation. -24 + 24 + 8z = 11 + 24 Combine like terms: -24 + 24 = 0 0 + 8z = 11 + 24 8z = 11 + 24 Combine like terms: 11 + 24 = 35 8z = 35 Divide each side by '8'. z = 4.375 Simplifying z = 4.375
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