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Simplifying 10z + -6(3z + 4) = 5(2z + (3z + 4) + -22) Reorder the terms: 10z + -6(4 + 3z) = 5(2z + (3z + 4) + -22) 10z + (4 * -6 + 3z * -6) = 5(2z + (3z + 4) + -22) 10z + (-24 + -18z) = 5(2z + (3z + 4) + -22) Reorder the terms: -24 + 10z + -18z = 5(2z + (3z + 4) + -22) Combine like terms: 10z + -18z = -8z -24 + -8z = 5(2z + (3z + 4) + -22) Reorder the terms: -24 + -8z = 5(2z + (4 + 3z) + -22) Remove parenthesis around (4 + 3z) -24 + -8z = 5(2z + 4 + 3z + -22) Reorder the terms: -24 + -8z = 5(4 + -22 + 2z + 3z) Combine like terms: 4 + -22 = -18 -24 + -8z = 5(-18 + 2z + 3z) Combine like terms: 2z + 3z = 5z -24 + -8z = 5(-18 + 5z) -24 + -8z = (-18 * 5 + 5z * 5) -24 + -8z = (-90 + 25z) Solving -24 + -8z = -90 + 25z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-25z' to each side of the equation. -24 + -8z + -25z = -90 + 25z + -25z Combine like terms: -8z + -25z = -33z -24 + -33z = -90 + 25z + -25z Combine like terms: 25z + -25z = 0 -24 + -33z = -90 + 0 -24 + -33z = -90 Add '24' to each side of the equation. -24 + 24 + -33z = -90 + 24 Combine like terms: -24 + 24 = 0 0 + -33z = -90 + 24 -33z = -90 + 24 Combine like terms: -90 + 24 = -66 -33z = -66 Divide each side by '-33'. z = 2 Simplifying z = 2
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