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Simplifying 7(z + -6) + -1(5 + 9z) = -3z Reorder the terms: 7(-6 + z) + -1(5 + 9z) = -3z (-6 * 7 + z * 7) + -1(5 + 9z) = -3z (-42 + 7z) + -1(5 + 9z) = -3z -42 + 7z + (5 * -1 + 9z * -1) = -3z -42 + 7z + (-5 + -9z) = -3z Reorder the terms: -42 + -5 + 7z + -9z = -3z Combine like terms: -42 + -5 = -47 -47 + 7z + -9z = -3z Combine like terms: 7z + -9z = -2z -47 + -2z = -3z Solving -47 + -2z = -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. -47 + -2z + 3z = -3z + 3z Combine like terms: -2z + 3z = 1z -47 + 1z = -3z + 3z Combine like terms: -3z + 3z = 0 -47 + 1z = 0 Add '47' to each side of the equation. -47 + 47 + 1z = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 1z = 0 + 47 1z = 0 + 47 Combine like terms: 0 + 47 = 47 1z = 47 Divide each side by '1'. z = 47 Simplifying z = 47
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