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Simplifying 8[z + -1(6z + 55) + 10] = 3(z + 9) Reorder the terms: 8[z + -1(55 + 6z) + 10] = 3(z + 9) 8[z + (55 * -1 + 6z * -1) + 10] = 3(z + 9) 8[z + (-55 + -6z) + 10] = 3(z + 9) Reorder the terms: 8[-55 + 10 + z + -6z] = 3(z + 9) Combine like terms: -55 + 10 = -45 8[-45 + z + -6z] = 3(z + 9) Combine like terms: z + -6z = -5z 8[-45 + -5z] = 3(z + 9) [-45 * 8 + -5z * 8] = 3(z + 9) [-360 + -40z] = 3(z + 9) Reorder the terms: -360 + -40z = 3(9 + z) -360 + -40z = (9 * 3 + z * 3) -360 + -40z = (27 + 3z) Solving -360 + -40z = 27 + 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. -360 + -40z + -3z = 27 + 3z + -3z Combine like terms: -40z + -3z = -43z -360 + -43z = 27 + 3z + -3z Combine like terms: 3z + -3z = 0 -360 + -43z = 27 + 0 -360 + -43z = 27 Add '360' to each side of the equation. -360 + 360 + -43z = 27 + 360 Combine like terms: -360 + 360 = 0 0 + -43z = 27 + 360 -43z = 27 + 360 Combine like terms: 27 + 360 = 387 -43z = 387 Divide each side by '-43'. z = -9 Simplifying z = -9
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