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Simplifying 4(6z + -1) + -5(z + 7) = 16(z + 1) Reorder the terms: 4(-1 + 6z) + -5(z + 7) = 16(z + 1) (-1 * 4 + 6z * 4) + -5(z + 7) = 16(z + 1) (-4 + 24z) + -5(z + 7) = 16(z + 1) Reorder the terms: -4 + 24z + -5(7 + z) = 16(z + 1) -4 + 24z + (7 * -5 + z * -5) = 16(z + 1) -4 + 24z + (-35 + -5z) = 16(z + 1) Reorder the terms: -4 + -35 + 24z + -5z = 16(z + 1) Combine like terms: -4 + -35 = -39 -39 + 24z + -5z = 16(z + 1) Combine like terms: 24z + -5z = 19z -39 + 19z = 16(z + 1) Reorder the terms: -39 + 19z = 16(1 + z) -39 + 19z = (1 * 16 + z * 16) -39 + 19z = (16 + 16z) Solving -39 + 19z = 16 + 16z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-16z' to each side of the equation. -39 + 19z + -16z = 16 + 16z + -16z Combine like terms: 19z + -16z = 3z -39 + 3z = 16 + 16z + -16z Combine like terms: 16z + -16z = 0 -39 + 3z = 16 + 0 -39 + 3z = 16 Add '39' to each side of the equation. -39 + 39 + 3z = 16 + 39 Combine like terms: -39 + 39 = 0 0 + 3z = 16 + 39 3z = 16 + 39 Combine like terms: 16 + 39 = 55 3z = 55 Divide each side by '3'. z = 18.33333333 Simplifying z = 18.33333333
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