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Simplifying 2(6z + -1) + -5(z + 1) = 2(z + 1) Reorder the terms: 2(-1 + 6z) + -5(z + 1) = 2(z + 1) (-1 * 2 + 6z * 2) + -5(z + 1) = 2(z + 1) (-2 + 12z) + -5(z + 1) = 2(z + 1) Reorder the terms: -2 + 12z + -5(1 + z) = 2(z + 1) -2 + 12z + (1 * -5 + z * -5) = 2(z + 1) -2 + 12z + (-5 + -5z) = 2(z + 1) Reorder the terms: -2 + -5 + 12z + -5z = 2(z + 1) Combine like terms: -2 + -5 = -7 -7 + 12z + -5z = 2(z + 1) Combine like terms: 12z + -5z = 7z -7 + 7z = 2(z + 1) Reorder the terms: -7 + 7z = 2(1 + z) -7 + 7z = (1 * 2 + z * 2) -7 + 7z = (2 + 2z) Solving -7 + 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. -7 + 7z + -2z = 2 + 2z + -2z Combine like terms: 7z + -2z = 5z -7 + 5z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -7 + 5z = 2 + 0 -7 + 5z = 2 Add '7' to each side of the equation. -7 + 7 + 5z = 2 + 7 Combine like terms: -7 + 7 = 0 0 + 5z = 2 + 7 5z = 2 + 7 Combine like terms: 2 + 7 = 9 5z = 9 Divide each side by '5'. z = 1.8 Simplifying z = 1.8
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