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Simplifying -10(z + 1) + 5(3z + -4) = 4(z + -3) + 9 Reorder the terms: -10(1 + z) + 5(3z + -4) = 4(z + -3) + 9 (1 * -10 + z * -10) + 5(3z + -4) = 4(z + -3) + 9 (-10 + -10z) + 5(3z + -4) = 4(z + -3) + 9 Reorder the terms: -10 + -10z + 5(-4 + 3z) = 4(z + -3) + 9 -10 + -10z + (-4 * 5 + 3z * 5) = 4(z + -3) + 9 -10 + -10z + (-20 + 15z) = 4(z + -3) + 9 Reorder the terms: -10 + -20 + -10z + 15z = 4(z + -3) + 9 Combine like terms: -10 + -20 = -30 -30 + -10z + 15z = 4(z + -3) + 9 Combine like terms: -10z + 15z = 5z -30 + 5z = 4(z + -3) + 9 Reorder the terms: -30 + 5z = 4(-3 + z) + 9 -30 + 5z = (-3 * 4 + z * 4) + 9 -30 + 5z = (-12 + 4z) + 9 Reorder the terms: -30 + 5z = -12 + 9 + 4z Combine like terms: -12 + 9 = -3 -30 + 5z = -3 + 4z Solving -30 + 5z = -3 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -30 + 5z + -4z = -3 + 4z + -4z Combine like terms: 5z + -4z = 1z -30 + 1z = -3 + 4z + -4z Combine like terms: 4z + -4z = 0 -30 + 1z = -3 + 0 -30 + 1z = -3 Add '30' to each side of the equation. -30 + 30 + 1z = -3 + 30 Combine like terms: -30 + 30 = 0 0 + 1z = -3 + 30 1z = -3 + 30 Combine like terms: -3 + 30 = 27 1z = 27 Divide each side by '1'. z = 27 Simplifying z = 27
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