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Simplifying 7[z + -1(9z + 82) + 2] = 3(z + 10) Reorder the terms: 7[z + -1(82 + 9z) + 2] = 3(z + 10) 7[z + (82 * -1 + 9z * -1) + 2] = 3(z + 10) 7[z + (-82 + -9z) + 2] = 3(z + 10) Reorder the terms: 7[-82 + 2 + z + -9z] = 3(z + 10) Combine like terms: -82 + 2 = -80 7[-80 + z + -9z] = 3(z + 10) Combine like terms: z + -9z = -8z 7[-80 + -8z] = 3(z + 10) [-80 * 7 + -8z * 7] = 3(z + 10) [-560 + -56z] = 3(z + 10) Reorder the terms: -560 + -56z = 3(10 + z) -560 + -56z = (10 * 3 + z * 3) -560 + -56z = (30 + 3z) Solving -560 + -56z = 30 + 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. -560 + -56z + -3z = 30 + 3z + -3z Combine like terms: -56z + -3z = -59z -560 + -59z = 30 + 3z + -3z Combine like terms: 3z + -3z = 0 -560 + -59z = 30 + 0 -560 + -59z = 30 Add '560' to each side of the equation. -560 + 560 + -59z = 30 + 560 Combine like terms: -560 + 560 = 0 0 + -59z = 30 + 560 -59z = 30 + 560 Combine like terms: 30 + 560 = 590 -59z = 590 Divide each side by '-59'. z = -10 Simplifying z = -10
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