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Simplifying -15(z + 3) + 5(4z + -7) = 4(z + -3) + 13 Reorder the terms: -15(3 + z) + 5(4z + -7) = 4(z + -3) + 13 (3 * -15 + z * -15) + 5(4z + -7) = 4(z + -3) + 13 (-45 + -15z) + 5(4z + -7) = 4(z + -3) + 13 Reorder the terms: -45 + -15z + 5(-7 + 4z) = 4(z + -3) + 13 -45 + -15z + (-7 * 5 + 4z * 5) = 4(z + -3) + 13 -45 + -15z + (-35 + 20z) = 4(z + -3) + 13 Reorder the terms: -45 + -35 + -15z + 20z = 4(z + -3) + 13 Combine like terms: -45 + -35 = -80 -80 + -15z + 20z = 4(z + -3) + 13 Combine like terms: -15z + 20z = 5z -80 + 5z = 4(z + -3) + 13 Reorder the terms: -80 + 5z = 4(-3 + z) + 13 -80 + 5z = (-3 * 4 + z * 4) + 13 -80 + 5z = (-12 + 4z) + 13 Reorder the terms: -80 + 5z = -12 + 13 + 4z Combine like terms: -12 + 13 = 1 -80 + 5z = 1 + 4z Solving -80 + 5z = 1 + 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. -80 + 5z + -4z = 1 + 4z + -4z Combine like terms: 5z + -4z = 1z -80 + 1z = 1 + 4z + -4z Combine like terms: 4z + -4z = 0 -80 + 1z = 1 + 0 -80 + 1z = 1 Add '80' to each side of the equation. -80 + 80 + 1z = 1 + 80 Combine like terms: -80 + 80 = 0 0 + 1z = 1 + 80 1z = 1 + 80 Combine like terms: 1 + 80 = 81 1z = 81 Divide each side by '1'. z = 81 Simplifying z = 81
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