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Simplifying 9(2z + 7) + -7(z + 3) = 8(7 + -3z) + -2(6z + 7) Reorder the terms: 9(7 + 2z) + -7(z + 3) = 8(7 + -3z) + -2(6z + 7) (7 * 9 + 2z * 9) + -7(z + 3) = 8(7 + -3z) + -2(6z + 7) (63 + 18z) + -7(z + 3) = 8(7 + -3z) + -2(6z + 7) Reorder the terms: 63 + 18z + -7(3 + z) = 8(7 + -3z) + -2(6z + 7) 63 + 18z + (3 * -7 + z * -7) = 8(7 + -3z) + -2(6z + 7) 63 + 18z + (-21 + -7z) = 8(7 + -3z) + -2(6z + 7) Reorder the terms: 63 + -21 + 18z + -7z = 8(7 + -3z) + -2(6z + 7) Combine like terms: 63 + -21 = 42 42 + 18z + -7z = 8(7 + -3z) + -2(6z + 7) Combine like terms: 18z + -7z = 11z 42 + 11z = 8(7 + -3z) + -2(6z + 7) 42 + 11z = (7 * 8 + -3z * 8) + -2(6z + 7) 42 + 11z = (56 + -24z) + -2(6z + 7) Reorder the terms: 42 + 11z = 56 + -24z + -2(7 + 6z) 42 + 11z = 56 + -24z + (7 * -2 + 6z * -2) 42 + 11z = 56 + -24z + (-14 + -12z) Reorder the terms: 42 + 11z = 56 + -14 + -24z + -12z Combine like terms: 56 + -14 = 42 42 + 11z = 42 + -24z + -12z Combine like terms: -24z + -12z = -36z 42 + 11z = 42 + -36z Add '-42' to each side of the equation. 42 + -42 + 11z = 42 + -42 + -36z Combine like terms: 42 + -42 = 0 0 + 11z = 42 + -42 + -36z 11z = 42 + -42 + -36z Combine like terms: 42 + -42 = 0 11z = 0 + -36z 11z = -36z Solving 11z = -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. 11z + 36z = -36z + 36z Combine like terms: 11z + 36z = 47z 47z = -36z + 36z Combine like terms: -36z + 36z = 0 47z = 0 Divide each side by '47'. z = 0 Simplifying z = 0
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