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Simplifying -7(z + 1) + 4(3z + -3) = 4(z + -5) + 13 Reorder the terms: -7(1 + z) + 4(3z + -3) = 4(z + -5) + 13 (1 * -7 + z * -7) + 4(3z + -3) = 4(z + -5) + 13 (-7 + -7z) + 4(3z + -3) = 4(z + -5) + 13 Reorder the terms: -7 + -7z + 4(-3 + 3z) = 4(z + -5) + 13 -7 + -7z + (-3 * 4 + 3z * 4) = 4(z + -5) + 13 -7 + -7z + (-12 + 12z) = 4(z + -5) + 13 Reorder the terms: -7 + -12 + -7z + 12z = 4(z + -5) + 13 Combine like terms: -7 + -12 = -19 -19 + -7z + 12z = 4(z + -5) + 13 Combine like terms: -7z + 12z = 5z -19 + 5z = 4(z + -5) + 13 Reorder the terms: -19 + 5z = 4(-5 + z) + 13 -19 + 5z = (-5 * 4 + z * 4) + 13 -19 + 5z = (-20 + 4z) + 13 Reorder the terms: -19 + 5z = -20 + 13 + 4z Combine like terms: -20 + 13 = -7 -19 + 5z = -7 + 4z Solving -19 + 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. -19 + 5z + -4z = -7 + 4z + -4z Combine like terms: 5z + -4z = 1z -19 + 1z = -7 + 4z + -4z Combine like terms: 4z + -4z = 0 -19 + 1z = -7 + 0 -19 + 1z = -7 Add '19' to each side of the equation. -19 + 19 + 1z = -7 + 19 Combine like terms: -19 + 19 = 0 0 + 1z = -7 + 19 1z = -7 + 19 Combine like terms: -7 + 19 = 12 1z = 12 Divide each side by '1'. z = 12 Simplifying z = 12
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