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Simplifying 7(3z + 1) + -1 = 20(z + -2) + 47 Reorder the terms: 7(1 + 3z) + -1 = 20(z + -2) + 47 (1 * 7 + 3z * 7) + -1 = 20(z + -2) + 47 (7 + 21z) + -1 = 20(z + -2) + 47 Reorder the terms: 7 + -1 + 21z = 20(z + -2) + 47 Combine like terms: 7 + -1 = 6 6 + 21z = 20(z + -2) + 47 Reorder the terms: 6 + 21z = 20(-2 + z) + 47 6 + 21z = (-2 * 20 + z * 20) + 47 6 + 21z = (-40 + 20z) + 47 Reorder the terms: 6 + 21z = -40 + 47 + 20z Combine like terms: -40 + 47 = 7 6 + 21z = 7 + 20z Solving 6 + 21z = 7 + 20z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-20z' to each side of the equation. 6 + 21z + -20z = 7 + 20z + -20z Combine like terms: 21z + -20z = 1z 6 + 1z = 7 + 20z + -20z Combine like terms: 20z + -20z = 0 6 + 1z = 7 + 0 6 + 1z = 7 Add '-6' to each side of the equation. 6 + -6 + 1z = 7 + -6 Combine like terms: 6 + -6 = 0 0 + 1z = 7 + -6 1z = 7 + -6 Combine like terms: 7 + -6 = 1 1z = 1 Divide each side by '1'. z = 1 Simplifying z = 1
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