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Simplifying 35z + 4(7z + -42) = 18(2z + -3) + -3(z + -172) Reorder the terms: 35z + 4(-42 + 7z) = 18(2z + -3) + -3(z + -172) 35z + (-42 * 4 + 7z * 4) = 18(2z + -3) + -3(z + -172) 35z + (-168 + 28z) = 18(2z + -3) + -3(z + -172) Reorder the terms: -168 + 35z + 28z = 18(2z + -3) + -3(z + -172) Combine like terms: 35z + 28z = 63z -168 + 63z = 18(2z + -3) + -3(z + -172) Reorder the terms: -168 + 63z = 18(-3 + 2z) + -3(z + -172) -168 + 63z = (-3 * 18 + 2z * 18) + -3(z + -172) -168 + 63z = (-54 + 36z) + -3(z + -172) Reorder the terms: -168 + 63z = -54 + 36z + -3(-172 + z) -168 + 63z = -54 + 36z + (-172 * -3 + z * -3) -168 + 63z = -54 + 36z + (516 + -3z) Reorder the terms: -168 + 63z = -54 + 516 + 36z + -3z Combine like terms: -54 + 516 = 462 -168 + 63z = 462 + 36z + -3z Combine like terms: 36z + -3z = 33z -168 + 63z = 462 + 33z Solving -168 + 63z = 462 + 33z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-33z' to each side of the equation. -168 + 63z + -33z = 462 + 33z + -33z Combine like terms: 63z + -33z = 30z -168 + 30z = 462 + 33z + -33z Combine like terms: 33z + -33z = 0 -168 + 30z = 462 + 0 -168 + 30z = 462 Add '168' to each side of the equation. -168 + 168 + 30z = 462 + 168 Combine like terms: -168 + 168 = 0 0 + 30z = 462 + 168 30z = 462 + 168 Combine like terms: 462 + 168 = 630 30z = 630 Divide each side by '30'. z = 21 Simplifying z = 21
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