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Simplifying 10[z + -1(2z + 19) + 10] = 2(z + 9) Reorder the terms: 10[z + -1(19 + 2z) + 10] = 2(z + 9) 10[z + (19 * -1 + 2z * -1) + 10] = 2(z + 9) 10[z + (-19 + -2z) + 10] = 2(z + 9) Reorder the terms: 10[-19 + 10 + z + -2z] = 2(z + 9) Combine like terms: -19 + 10 = -9 10[-9 + z + -2z] = 2(z + 9) Combine like terms: z + -2z = -1z 10[-9 + -1z] = 2(z + 9) [-9 * 10 + -1z * 10] = 2(z + 9) [-90 + -10z] = 2(z + 9) Reorder the terms: -90 + -10z = 2(9 + z) -90 + -10z = (9 * 2 + z * 2) -90 + -10z = (18 + 2z) Solving -90 + -10z = 18 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -90 + -10z + -2z = 18 + 2z + -2z Combine like terms: -10z + -2z = -12z -90 + -12z = 18 + 2z + -2z Combine like terms: 2z + -2z = 0 -90 + -12z = 18 + 0 -90 + -12z = 18 Add '90' to each side of the equation. -90 + 90 + -12z = 18 + 90 Combine like terms: -90 + 90 = 0 0 + -12z = 18 + 90 -12z = 18 + 90 Combine like terms: 18 + 90 = 108 -12z = 108 Divide each side by '-12'. z = -9 Simplifying z = -9
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