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Simplifying 35z + 4(7z + -42) = 18(2z + -3) + -3(2 + -172) Reorder the terms: 35z + 4(-42 + 7z) = 18(2z + -3) + -3(2 + -172) 35z + (-42 * 4 + 7z * 4) = 18(2z + -3) + -3(2 + -172) 35z + (-168 + 28z) = 18(2z + -3) + -3(2 + -172) Reorder the terms: -168 + 35z + 28z = 18(2z + -3) + -3(2 + -172) Combine like terms: 35z + 28z = 63z -168 + 63z = 18(2z + -3) + -3(2 + -172) Reorder the terms: -168 + 63z = 18(-3 + 2z) + -3(2 + -172) -168 + 63z = (-3 * 18 + 2z * 18) + -3(2 + -172) -168 + 63z = (-54 + 36z) + -3(2 + -172) Combine like terms: 2 + -172 = -170 -168 + 63z = -54 + 36z + -3(-170) Multiply -3 * -170 -168 + 63z = -54 + 36z + 510 Reorder the terms: -168 + 63z = -54 + 510 + 36z Combine like terms: -54 + 510 = 456 -168 + 63z = 456 + 36z Solving -168 + 63z = 456 + 36z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-36z' to each side of the equation. -168 + 63z + -36z = 456 + 36z + -36z Combine like terms: 63z + -36z = 27z -168 + 27z = 456 + 36z + -36z Combine like terms: 36z + -36z = 0 -168 + 27z = 456 + 0 -168 + 27z = 456 Add '168' to each side of the equation. -168 + 168 + 27z = 456 + 168 Combine like terms: -168 + 168 = 0 0 + 27z = 456 + 168 27z = 456 + 168 Combine like terms: 456 + 168 = 624 27z = 624 Divide each side by '27'. z = 23.11111111 Simplifying z = 23.11111111
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