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Simplifying -4(z + 1) + 3(3z + -7) = 4(7 + -5) + 13 Reorder the terms: -4(1 + z) + 3(3z + -7) = 4(7 + -5) + 13 (1 * -4 + z * -4) + 3(3z + -7) = 4(7 + -5) + 13 (-4 + -4z) + 3(3z + -7) = 4(7 + -5) + 13 Reorder the terms: -4 + -4z + 3(-7 + 3z) = 4(7 + -5) + 13 -4 + -4z + (-7 * 3 + 3z * 3) = 4(7 + -5) + 13 -4 + -4z + (-21 + 9z) = 4(7 + -5) + 13 Reorder the terms: -4 + -21 + -4z + 9z = 4(7 + -5) + 13 Combine like terms: -4 + -21 = -25 -25 + -4z + 9z = 4(7 + -5) + 13 Combine like terms: -4z + 9z = 5z -25 + 5z = 4(7 + -5) + 13 Combine like terms: 7 + -5 = 2 -25 + 5z = 4(2) + 13 Multiply 4 * 2 -25 + 5z = 8 + 13 Combine like terms: 8 + 13 = 21 -25 + 5z = 21 Solving -25 + 5z = 21 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 5z = 21 + 25 Combine like terms: -25 + 25 = 0 0 + 5z = 21 + 25 5z = 21 + 25 Combine like terms: 21 + 25 = 46 5z = 46 Divide each side by '5'. z = 9.2 Simplifying z = 9.2
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