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Simplifying 5(4z + -1) + -4(z + 4) = 10(z + 1) Reorder the terms: 5(-1 + 4z) + -4(z + 4) = 10(z + 1) (-1 * 5 + 4z * 5) + -4(z + 4) = 10(z + 1) (-5 + 20z) + -4(z + 4) = 10(z + 1) Reorder the terms: -5 + 20z + -4(4 + z) = 10(z + 1) -5 + 20z + (4 * -4 + z * -4) = 10(z + 1) -5 + 20z + (-16 + -4z) = 10(z + 1) Reorder the terms: -5 + -16 + 20z + -4z = 10(z + 1) Combine like terms: -5 + -16 = -21 -21 + 20z + -4z = 10(z + 1) Combine like terms: 20z + -4z = 16z -21 + 16z = 10(z + 1) Reorder the terms: -21 + 16z = 10(1 + z) -21 + 16z = (1 * 10 + z * 10) -21 + 16z = (10 + 10z) Solving -21 + 16z = 10 + 10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10z' to each side of the equation. -21 + 16z + -10z = 10 + 10z + -10z Combine like terms: 16z + -10z = 6z -21 + 6z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -21 + 6z = 10 + 0 -21 + 6z = 10 Add '21' to each side of the equation. -21 + 21 + 6z = 10 + 21 Combine like terms: -21 + 21 = 0 0 + 6z = 10 + 21 6z = 10 + 21 Combine like terms: 10 + 21 = 31 6z = 31 Divide each side by '6'. z = 5.166666667 Simplifying z = 5.166666667
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