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Simplifying 2.7(z + -7) + 6 = 2.1(3z + 1) Reorder the terms: 2.7(-7 + z) + 6 = 2.1(3z + 1) (-7 * 2.7 + z * 2.7) + 6 = 2.1(3z + 1) (-18.9 + 2.7z) + 6 = 2.1(3z + 1) Reorder the terms: -18.9 + 6 + 2.7z = 2.1(3z + 1) Combine like terms: -18.9 + 6 = -12.9 -12.9 + 2.7z = 2.1(3z + 1) Reorder the terms: -12.9 + 2.7z = 2.1(1 + 3z) -12.9 + 2.7z = (1 * 2.1 + 3z * 2.1) -12.9 + 2.7z = (2.1 + 6.3z) Solving -12.9 + 2.7z = 2.1 + 6.3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6.3z' to each side of the equation. -12.9 + 2.7z + -6.3z = 2.1 + 6.3z + -6.3z Combine like terms: 2.7z + -6.3z = -3.6z -12.9 + -3.6z = 2.1 + 6.3z + -6.3z Combine like terms: 6.3z + -6.3z = 0.0 -12.9 + -3.6z = 2.1 + 0.0 -12.9 + -3.6z = 2.1 Add '12.9' to each side of the equation. -12.9 + 12.9 + -3.6z = 2.1 + 12.9 Combine like terms: -12.9 + 12.9 = 0.0 0.0 + -3.6z = 2.1 + 12.9 -3.6z = 2.1 + 12.9 Combine like terms: 2.1 + 12.9 = 15 -3.6z = 15 Divide each side by '-3.6'. z = -4.166666667 Simplifying z = -4.166666667
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