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Simplifying 2[3 + -1(5 + -5r)] + -1r = -10 + 3(z + 3r) 2[3 + (5 * -1 + -5r * -1)] + -1r = -10 + 3(z + 3r) 2[3 + (-5 + 5r)] + -1r = -10 + 3(z + 3r) Combine like terms: 3 + -5 = -2 2[-2 + 5r] + -1r = -10 + 3(z + 3r) [-2 * 2 + 5r * 2] + -1r = -10 + 3(z + 3r) [-4 + 10r] + -1r = -10 + 3(z + 3r) Combine like terms: 10r + -1r = 9r -4 + 9r = -10 + 3(z + 3r) Reorder the terms: -4 + 9r = -10 + 3(3r + z) -4 + 9r = -10 + (3r * 3 + z * 3) -4 + 9r = -10 + (9r + 3z) Add '-9r' to each side of the equation. -4 + 9r + -9r = -10 + 9r + -9r + 3z Combine like terms: 9r + -9r = 0 -4 + 0 = -10 + 9r + -9r + 3z -4 = -10 + 9r + -9r + 3z Combine like terms: 9r + -9r = 0 -4 = -10 + 0 + 3z -4 = -10 + 3z Solving -4 = -10 + 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. -4 + -3z = -10 + 3z + -3z Combine like terms: 3z + -3z = 0 -4 + -3z = -10 + 0 -4 + -3z = -10 Add '4' to each side of the equation. -4 + 4 + -3z = -10 + 4 Combine like terms: -4 + 4 = 0 0 + -3z = -10 + 4 -3z = -10 + 4 Combine like terms: -10 + 4 = -6 -3z = -6 Divide each side by '-3'. z = 2 Simplifying z = 2
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