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Simplifying -14(z + 1) + 6(3z + -4) = 3(z + -3) + 14 Reorder the terms: -14(1 + z) + 6(3z + -4) = 3(z + -3) + 14 (1 * -14 + z * -14) + 6(3z + -4) = 3(z + -3) + 14 (-14 + -14z) + 6(3z + -4) = 3(z + -3) + 14 Reorder the terms: -14 + -14z + 6(-4 + 3z) = 3(z + -3) + 14 -14 + -14z + (-4 * 6 + 3z * 6) = 3(z + -3) + 14 -14 + -14z + (-24 + 18z) = 3(z + -3) + 14 Reorder the terms: -14 + -24 + -14z + 18z = 3(z + -3) + 14 Combine like terms: -14 + -24 = -38 -38 + -14z + 18z = 3(z + -3) + 14 Combine like terms: -14z + 18z = 4z -38 + 4z = 3(z + -3) + 14 Reorder the terms: -38 + 4z = 3(-3 + z) + 14 -38 + 4z = (-3 * 3 + z * 3) + 14 -38 + 4z = (-9 + 3z) + 14 Reorder the terms: -38 + 4z = -9 + 14 + 3z Combine like terms: -9 + 14 = 5 -38 + 4z = 5 + 3z Solving -38 + 4z = 5 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -38 + 4z + -3z = 5 + 3z + -3z Combine like terms: 4z + -3z = 1z -38 + 1z = 5 + 3z + -3z Combine like terms: 3z + -3z = 0 -38 + 1z = 5 + 0 -38 + 1z = 5 Add '38' to each side of the equation. -38 + 38 + 1z = 5 + 38 Combine like terms: -38 + 38 = 0 0 + 1z = 5 + 38 1z = 5 + 38 Combine like terms: 5 + 38 = 43 1z = 43 Divide each side by '1'. z = 43 Simplifying z = 43
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