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Simplifying 3(6z + -1) + -4(z + 4) = 10(2 + 1) Reorder the terms: 3(-1 + 6z) + -4(z + 4) = 10(2 + 1) (-1 * 3 + 6z * 3) + -4(z + 4) = 10(2 + 1) (-3 + 18z) + -4(z + 4) = 10(2 + 1) Reorder the terms: -3 + 18z + -4(4 + z) = 10(2 + 1) -3 + 18z + (4 * -4 + z * -4) = 10(2 + 1) -3 + 18z + (-16 + -4z) = 10(2 + 1) Reorder the terms: -3 + -16 + 18z + -4z = 10(2 + 1) Combine like terms: -3 + -16 = -19 -19 + 18z + -4z = 10(2 + 1) Combine like terms: 18z + -4z = 14z -19 + 14z = 10(2 + 1) Combine like terms: 2 + 1 = 3 -19 + 14z = 10(3) Multiply 10 * 3 -19 + 14z = 30 Solving -19 + 14z = 30 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 14z = 30 + 19 Combine like terms: -19 + 19 = 0 0 + 14z = 30 + 19 14z = 30 + 19 Combine like terms: 30 + 19 = 49 14z = 49 Divide each side by '14'. z = 3.5 Simplifying z = 3.5
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