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Simplifying -8(z + 1) + 4(3z + -7) = 3(z + -3) + 13 Reorder the terms: -8(1 + z) + 4(3z + -7) = 3(z + -3) + 13 (1 * -8 + z * -8) + 4(3z + -7) = 3(z + -3) + 13 (-8 + -8z) + 4(3z + -7) = 3(z + -3) + 13 Reorder the terms: -8 + -8z + 4(-7 + 3z) = 3(z + -3) + 13 -8 + -8z + (-7 * 4 + 3z * 4) = 3(z + -3) + 13 -8 + -8z + (-28 + 12z) = 3(z + -3) + 13 Reorder the terms: -8 + -28 + -8z + 12z = 3(z + -3) + 13 Combine like terms: -8 + -28 = -36 -36 + -8z + 12z = 3(z + -3) + 13 Combine like terms: -8z + 12z = 4z -36 + 4z = 3(z + -3) + 13 Reorder the terms: -36 + 4z = 3(-3 + z) + 13 -36 + 4z = (-3 * 3 + z * 3) + 13 -36 + 4z = (-9 + 3z) + 13 Reorder the terms: -36 + 4z = -9 + 13 + 3z Combine like terms: -9 + 13 = 4 -36 + 4z = 4 + 3z Solving -36 + 4z = 4 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -36 + 4z + -3z = 4 + 3z + -3z Combine like terms: 4z + -3z = 1z -36 + 1z = 4 + 3z + -3z Combine like terms: 3z + -3z = 0 -36 + 1z = 4 + 0 -36 + 1z = 4 Add '36' to each side of the equation. -36 + 36 + 1z = 4 + 36 Combine like terms: -36 + 36 = 0 0 + 1z = 4 + 36 1z = 4 + 36 Combine like terms: 4 + 36 = 40 1z = 40 Divide each side by '1'. z = 40 Simplifying z = 40
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