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Simplifying 4(5z + -1) + -5(z + 3) = 10(z + 1) Reorder the terms: 4(-1 + 5z) + -5(z + 3) = 10(z + 1) (-1 * 4 + 5z * 4) + -5(z + 3) = 10(z + 1) (-4 + 20z) + -5(z + 3) = 10(z + 1) Reorder the terms: -4 + 20z + -5(3 + z) = 10(z + 1) -4 + 20z + (3 * -5 + z * -5) = 10(z + 1) -4 + 20z + (-15 + -5z) = 10(z + 1) Reorder the terms: -4 + -15 + 20z + -5z = 10(z + 1) Combine like terms: -4 + -15 = -19 -19 + 20z + -5z = 10(z + 1) Combine like terms: 20z + -5z = 15z -19 + 15z = 10(z + 1) Reorder the terms: -19 + 15z = 10(1 + z) -19 + 15z = (1 * 10 + z * 10) -19 + 15z = (10 + 10z) Solving -19 + 15z = 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. -19 + 15z + -10z = 10 + 10z + -10z Combine like terms: 15z + -10z = 5z -19 + 5z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -19 + 5z = 10 + 0 -19 + 5z = 10 Add '19' to each side of the equation. -19 + 19 + 5z = 10 + 19 Combine like terms: -19 + 19 = 0 0 + 5z = 10 + 19 5z = 10 + 19 Combine like terms: 10 + 19 = 29 5z = 29 Divide each side by '5'. z = 5.8 Simplifying z = 5.8
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