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Simplifying 4(5z + -1) + -2(z + 4) = 11(z + 1) Reorder the terms: 4(-1 + 5z) + -2(z + 4) = 11(z + 1) (-1 * 4 + 5z * 4) + -2(z + 4) = 11(z + 1) (-4 + 20z) + -2(z + 4) = 11(z + 1) Reorder the terms: -4 + 20z + -2(4 + z) = 11(z + 1) -4 + 20z + (4 * -2 + z * -2) = 11(z + 1) -4 + 20z + (-8 + -2z) = 11(z + 1) Reorder the terms: -4 + -8 + 20z + -2z = 11(z + 1) Combine like terms: -4 + -8 = -12 -12 + 20z + -2z = 11(z + 1) Combine like terms: 20z + -2z = 18z -12 + 18z = 11(z + 1) Reorder the terms: -12 + 18z = 11(1 + z) -12 + 18z = (1 * 11 + z * 11) -12 + 18z = (11 + 11z) Solving -12 + 18z = 11 + 11z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11z' to each side of the equation. -12 + 18z + -11z = 11 + 11z + -11z Combine like terms: 18z + -11z = 7z -12 + 7z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -12 + 7z = 11 + 0 -12 + 7z = 11 Add '12' to each side of the equation. -12 + 12 + 7z = 11 + 12 Combine like terms: -12 + 12 = 0 0 + 7z = 11 + 12 7z = 11 + 12 Combine like terms: 11 + 12 = 23 7z = 23 Divide each side by '7'. z = 3.285714286 Simplifying z = 3.285714286
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