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Simplifying -4(z + 1) + 3(3z + -7) = 4(z + -5) + 13 Reorder the terms: -4(1 + z) + 3(3z + -7) = 4(z + -5) + 13 (1 * -4 + z * -4) + 3(3z + -7) = 4(z + -5) + 13 (-4 + -4z) + 3(3z + -7) = 4(z + -5) + 13 Reorder the terms: -4 + -4z + 3(-7 + 3z) = 4(z + -5) + 13 -4 + -4z + (-7 * 3 + 3z * 3) = 4(z + -5) + 13 -4 + -4z + (-21 + 9z) = 4(z + -5) + 13 Reorder the terms: -4 + -21 + -4z + 9z = 4(z + -5) + 13 Combine like terms: -4 + -21 = -25 -25 + -4z + 9z = 4(z + -5) + 13 Combine like terms: -4z + 9z = 5z -25 + 5z = 4(z + -5) + 13 Reorder the terms: -25 + 5z = 4(-5 + z) + 13 -25 + 5z = (-5 * 4 + z * 4) + 13 -25 + 5z = (-20 + 4z) + 13 Reorder the terms: -25 + 5z = -20 + 13 + 4z Combine like terms: -20 + 13 = -7 -25 + 5z = -7 + 4z Solving -25 + 5z = -7 + 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. -25 + 5z + -4z = -7 + 4z + -4z Combine like terms: 5z + -4z = 1z -25 + 1z = -7 + 4z + -4z Combine like terms: 4z + -4z = 0 -25 + 1z = -7 + 0 -25 + 1z = -7 Add '25' to each side of the equation. -25 + 25 + 1z = -7 + 25 Combine like terms: -25 + 25 = 0 0 + 1z = -7 + 25 1z = -7 + 25 Combine like terms: -7 + 25 = 18 1z = 18 Divide each side by '1'. z = 18 Simplifying z = 18
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