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Simplifying 3(2z + -7) + -1 = 4(3z + 1) + 1 Reorder the terms: 3(-7 + 2z) + -1 = 4(3z + 1) + 1 (-7 * 3 + 2z * 3) + -1 = 4(3z + 1) + 1 (-21 + 6z) + -1 = 4(3z + 1) + 1 Reorder the terms: -21 + -1 + 6z = 4(3z + 1) + 1 Combine like terms: -21 + -1 = -22 -22 + 6z = 4(3z + 1) + 1 Reorder the terms: -22 + 6z = 4(1 + 3z) + 1 -22 + 6z = (1 * 4 + 3z * 4) + 1 -22 + 6z = (4 + 12z) + 1 Reorder the terms: -22 + 6z = 4 + 1 + 12z Combine like terms: 4 + 1 = 5 -22 + 6z = 5 + 12z Solving -22 + 6z = 5 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -22 + 6z + -12z = 5 + 12z + -12z Combine like terms: 6z + -12z = -6z -22 + -6z = 5 + 12z + -12z Combine like terms: 12z + -12z = 0 -22 + -6z = 5 + 0 -22 + -6z = 5 Add '22' to each side of the equation. -22 + 22 + -6z = 5 + 22 Combine like terms: -22 + 22 = 0 0 + -6z = 5 + 22 -6z = 5 + 22 Combine like terms: 5 + 22 = 27 -6z = 27 Divide each side by '-6'. z = -4.5 Simplifying z = -4.5
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