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Simplifying 4(z + -5) + -2(3z + 7) = 3(-2z + 9) Reorder the terms: 4(-5 + z) + -2(3z + 7) = 3(-2z + 9) (-5 * 4 + z * 4) + -2(3z + 7) = 3(-2z + 9) (-20 + 4z) + -2(3z + 7) = 3(-2z + 9) Reorder the terms: -20 + 4z + -2(7 + 3z) = 3(-2z + 9) -20 + 4z + (7 * -2 + 3z * -2) = 3(-2z + 9) -20 + 4z + (-14 + -6z) = 3(-2z + 9) Reorder the terms: -20 + -14 + 4z + -6z = 3(-2z + 9) Combine like terms: -20 + -14 = -34 -34 + 4z + -6z = 3(-2z + 9) Combine like terms: 4z + -6z = -2z -34 + -2z = 3(-2z + 9) Reorder the terms: -34 + -2z = 3(9 + -2z) -34 + -2z = (9 * 3 + -2z * 3) -34 + -2z = (27 + -6z) Solving -34 + -2z = 27 + -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. -34 + -2z + 6z = 27 + -6z + 6z Combine like terms: -2z + 6z = 4z -34 + 4z = 27 + -6z + 6z Combine like terms: -6z + 6z = 0 -34 + 4z = 27 + 0 -34 + 4z = 27 Add '34' to each side of the equation. -34 + 34 + 4z = 27 + 34 Combine like terms: -34 + 34 = 0 0 + 4z = 27 + 34 4z = 27 + 34 Combine like terms: 27 + 34 = 61 4z = 61 Divide each side by '4'. z = 15.25 Simplifying z = 15.25
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