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Simplifying 6(3z + -1) + -3(z + 5) = 10(z + 1) Reorder the terms: 6(-1 + 3z) + -3(z + 5) = 10(z + 1) (-1 * 6 + 3z * 6) + -3(z + 5) = 10(z + 1) (-6 + 18z) + -3(z + 5) = 10(z + 1) Reorder the terms: -6 + 18z + -3(5 + z) = 10(z + 1) -6 + 18z + (5 * -3 + z * -3) = 10(z + 1) -6 + 18z + (-15 + -3z) = 10(z + 1) Reorder the terms: -6 + -15 + 18z + -3z = 10(z + 1) Combine like terms: -6 + -15 = -21 -21 + 18z + -3z = 10(z + 1) Combine like terms: 18z + -3z = 15z -21 + 15z = 10(z + 1) Reorder the terms: -21 + 15z = 10(1 + z) -21 + 15z = (1 * 10 + z * 10) -21 + 15z = (10 + 10z) Solving -21 + 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. -21 + 15z + -10z = 10 + 10z + -10z Combine like terms: 15z + -10z = 5z -21 + 5z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -21 + 5z = 10 + 0 -21 + 5z = 10 Add '21' to each side of the equation. -21 + 21 + 5z = 10 + 21 Combine like terms: -21 + 21 = 0 0 + 5z = 10 + 21 5z = 10 + 21 Combine like terms: 10 + 21 = 31 5z = 31 Divide each side by '5'. z = 6.2 Simplifying z = 6.2
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