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Simplifying -14(z + 3) + 6(3z + -4) = 3(z + -5) + 11 Reorder the terms: -14(3 + z) + 6(3z + -4) = 3(z + -5) + 11 (3 * -14 + z * -14) + 6(3z + -4) = 3(z + -5) + 11 (-42 + -14z) + 6(3z + -4) = 3(z + -5) + 11 Reorder the terms: -42 + -14z + 6(-4 + 3z) = 3(z + -5) + 11 -42 + -14z + (-4 * 6 + 3z * 6) = 3(z + -5) + 11 -42 + -14z + (-24 + 18z) = 3(z + -5) + 11 Reorder the terms: -42 + -24 + -14z + 18z = 3(z + -5) + 11 Combine like terms: -42 + -24 = -66 -66 + -14z + 18z = 3(z + -5) + 11 Combine like terms: -14z + 18z = 4z -66 + 4z = 3(z + -5) + 11 Reorder the terms: -66 + 4z = 3(-5 + z) + 11 -66 + 4z = (-5 * 3 + z * 3) + 11 -66 + 4z = (-15 + 3z) + 11 Reorder the terms: -66 + 4z = -15 + 11 + 3z Combine like terms: -15 + 11 = -4 -66 + 4z = -4 + 3z Solving -66 + 4z = -4 + 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. -66 + 4z + -3z = -4 + 3z + -3z Combine like terms: 4z + -3z = 1z -66 + 1z = -4 + 3z + -3z Combine like terms: 3z + -3z = 0 -66 + 1z = -4 + 0 -66 + 1z = -4 Add '66' to each side of the equation. -66 + 66 + 1z = -4 + 66 Combine like terms: -66 + 66 = 0 0 + 1z = -4 + 66 1z = -4 + 66 Combine like terms: -4 + 66 = 62 1z = 62 Divide each side by '1'. z = 62 Simplifying z = 62
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