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Simplifying 6 + 7(-3z + 4) = -9(4z + -7) + 6 Reorder the terms: 6 + 7(4 + -3z) = -9(4z + -7) + 6 6 + (4 * 7 + -3z * 7) = -9(4z + -7) + 6 6 + (28 + -21z) = -9(4z + -7) + 6 Combine like terms: 6 + 28 = 34 34 + -21z = -9(4z + -7) + 6 Reorder the terms: 34 + -21z = -9(-7 + 4z) + 6 34 + -21z = (-7 * -9 + 4z * -9) + 6 34 + -21z = (63 + -36z) + 6 Reorder the terms: 34 + -21z = 63 + 6 + -36z Combine like terms: 63 + 6 = 69 34 + -21z = 69 + -36z Solving 34 + -21z = 69 + -36z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '36z' to each side of the equation. 34 + -21z + 36z = 69 + -36z + 36z Combine like terms: -21z + 36z = 15z 34 + 15z = 69 + -36z + 36z Combine like terms: -36z + 36z = 0 34 + 15z = 69 + 0 34 + 15z = 69 Add '-34' to each side of the equation. 34 + -34 + 15z = 69 + -34 Combine like terms: 34 + -34 = 0 0 + 15z = 69 + -34 15z = 69 + -34 Combine like terms: 69 + -34 = 35 15z = 35 Divide each side by '15'. z = 2.333333333 Simplifying z = 2.333333333
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