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Simplifying 3(6z + -1) + -4(z + 5) = 7(z + 1) Reorder the terms: 3(-1 + 6z) + -4(z + 5) = 7(z + 1) (-1 * 3 + 6z * 3) + -4(z + 5) = 7(z + 1) (-3 + 18z) + -4(z + 5) = 7(z + 1) Reorder the terms: -3 + 18z + -4(5 + z) = 7(z + 1) -3 + 18z + (5 * -4 + z * -4) = 7(z + 1) -3 + 18z + (-20 + -4z) = 7(z + 1) Reorder the terms: -3 + -20 + 18z + -4z = 7(z + 1) Combine like terms: -3 + -20 = -23 -23 + 18z + -4z = 7(z + 1) Combine like terms: 18z + -4z = 14z -23 + 14z = 7(z + 1) Reorder the terms: -23 + 14z = 7(1 + z) -23 + 14z = (1 * 7 + z * 7) -23 + 14z = (7 + 7z) Solving -23 + 14z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -23 + 14z + -7z = 7 + 7z + -7z Combine like terms: 14z + -7z = 7z -23 + 7z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -23 + 7z = 7 + 0 -23 + 7z = 7 Add '23' to each side of the equation. -23 + 23 + 7z = 7 + 23 Combine like terms: -23 + 23 = 0 0 + 7z = 7 + 23 7z = 7 + 23 Combine like terms: 7 + 23 = 30 7z = 30 Divide each side by '7'. z = 4.285714286 Simplifying z = 4.285714286
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