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Simplifying 6(2z + -1) + -5(z + 3) = 2(z + 1) Reorder the terms: 6(-1 + 2z) + -5(z + 3) = 2(z + 1) (-1 * 6 + 2z * 6) + -5(z + 3) = 2(z + 1) (-6 + 12z) + -5(z + 3) = 2(z + 1) Reorder the terms: -6 + 12z + -5(3 + z) = 2(z + 1) -6 + 12z + (3 * -5 + z * -5) = 2(z + 1) -6 + 12z + (-15 + -5z) = 2(z + 1) Reorder the terms: -6 + -15 + 12z + -5z = 2(z + 1) Combine like terms: -6 + -15 = -21 -21 + 12z + -5z = 2(z + 1) Combine like terms: 12z + -5z = 7z -21 + 7z = 2(z + 1) Reorder the terms: -21 + 7z = 2(1 + z) -21 + 7z = (1 * 2 + z * 2) -21 + 7z = (2 + 2z) Solving -21 + 7z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -21 + 7z + -2z = 2 + 2z + -2z Combine like terms: 7z + -2z = 5z -21 + 5z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -21 + 5z = 2 + 0 -21 + 5z = 2 Add '21' to each side of the equation. -21 + 21 + 5z = 2 + 21 Combine like terms: -21 + 21 = 0 0 + 5z = 2 + 21 5z = 2 + 21 Combine like terms: 2 + 21 = 23 5z = 23 Divide each side by '5'. z = 4.6 Simplifying z = 4.6
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