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Simplifying 6z + -7 = -31 + 6(7z + -2) Reorder the terms: -7 + 6z = -31 + 6(7z + -2) Reorder the terms: -7 + 6z = -31 + 6(-2 + 7z) -7 + 6z = -31 + (-2 * 6 + 7z * 6) -7 + 6z = -31 + (-12 + 42z) Combine like terms: -31 + -12 = -43 -7 + 6z = -43 + 42z Solving -7 + 6z = -43 + 42z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-42z' to each side of the equation. -7 + 6z + -42z = -43 + 42z + -42z Combine like terms: 6z + -42z = -36z -7 + -36z = -43 + 42z + -42z Combine like terms: 42z + -42z = 0 -7 + -36z = -43 + 0 -7 + -36z = -43 Add '7' to each side of the equation. -7 + 7 + -36z = -43 + 7 Combine like terms: -7 + 7 = 0 0 + -36z = -43 + 7 -36z = -43 + 7 Combine like terms: -43 + 7 = -36 -36z = -36 Divide each side by '-36'. z = 1 Simplifying z = 1
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