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Simplifying -11(z + 2) + 6(3z + -3) = 6(z + -4) + 14 Reorder the terms: -11(2 + z) + 6(3z + -3) = 6(z + -4) + 14 (2 * -11 + z * -11) + 6(3z + -3) = 6(z + -4) + 14 (-22 + -11z) + 6(3z + -3) = 6(z + -4) + 14 Reorder the terms: -22 + -11z + 6(-3 + 3z) = 6(z + -4) + 14 -22 + -11z + (-3 * 6 + 3z * 6) = 6(z + -4) + 14 -22 + -11z + (-18 + 18z) = 6(z + -4) + 14 Reorder the terms: -22 + -18 + -11z + 18z = 6(z + -4) + 14 Combine like terms: -22 + -18 = -40 -40 + -11z + 18z = 6(z + -4) + 14 Combine like terms: -11z + 18z = 7z -40 + 7z = 6(z + -4) + 14 Reorder the terms: -40 + 7z = 6(-4 + z) + 14 -40 + 7z = (-4 * 6 + z * 6) + 14 -40 + 7z = (-24 + 6z) + 14 Reorder the terms: -40 + 7z = -24 + 14 + 6z Combine like terms: -24 + 14 = -10 -40 + 7z = -10 + 6z Solving -40 + 7z = -10 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -40 + 7z + -6z = -10 + 6z + -6z Combine like terms: 7z + -6z = 1z -40 + 1z = -10 + 6z + -6z Combine like terms: 6z + -6z = 0 -40 + 1z = -10 + 0 -40 + 1z = -10 Add '40' to each side of the equation. -40 + 40 + 1z = -10 + 40 Combine like terms: -40 + 40 = 0 0 + 1z = -10 + 40 1z = -10 + 40 Combine like terms: -10 + 40 = 30 1z = 30 Divide each side by '1'. z = 30 Simplifying z = 30
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