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Simplifying 3(2z + -6) + -4(3z + 1) = 5 + -2(z + 1) Reorder the terms: 3(-6 + 2z) + -4(3z + 1) = 5 + -2(z + 1) (-6 * 3 + 2z * 3) + -4(3z + 1) = 5 + -2(z + 1) (-18 + 6z) + -4(3z + 1) = 5 + -2(z + 1) Reorder the terms: -18 + 6z + -4(1 + 3z) = 5 + -2(z + 1) -18 + 6z + (1 * -4 + 3z * -4) = 5 + -2(z + 1) -18 + 6z + (-4 + -12z) = 5 + -2(z + 1) Reorder the terms: -18 + -4 + 6z + -12z = 5 + -2(z + 1) Combine like terms: -18 + -4 = -22 -22 + 6z + -12z = 5 + -2(z + 1) Combine like terms: 6z + -12z = -6z -22 + -6z = 5 + -2(z + 1) Reorder the terms: -22 + -6z = 5 + -2(1 + z) -22 + -6z = 5 + (1 * -2 + z * -2) -22 + -6z = 5 + (-2 + -2z) Combine like terms: 5 + -2 = 3 -22 + -6z = 3 + -2z Solving -22 + -6z = 3 + -2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2z' to each side of the equation. -22 + -6z + 2z = 3 + -2z + 2z Combine like terms: -6z + 2z = -4z -22 + -4z = 3 + -2z + 2z Combine like terms: -2z + 2z = 0 -22 + -4z = 3 + 0 -22 + -4z = 3 Add '22' to each side of the equation. -22 + 22 + -4z = 3 + 22 Combine like terms: -22 + 22 = 0 0 + -4z = 3 + 22 -4z = 3 + 22 Combine like terms: 3 + 22 = 25 -4z = 25 Divide each side by '-4'. z = -6.25 Simplifying z = -6.25
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