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Simplifying 10(z + 2) + -4(z + -3) = 3(z + -4) + 2(-4) Reorder the terms: 10(2 + z) + -4(z + -3) = 3(z + -4) + 2(-4) (2 * 10 + z * 10) + -4(z + -3) = 3(z + -4) + 2(-4) (20 + 10z) + -4(z + -3) = 3(z + -4) + 2(-4) Reorder the terms: 20 + 10z + -4(-3 + z) = 3(z + -4) + 2(-4) 20 + 10z + (-3 * -4 + z * -4) = 3(z + -4) + 2(-4) 20 + 10z + (12 + -4z) = 3(z + -4) + 2(-4) Reorder the terms: 20 + 12 + 10z + -4z = 3(z + -4) + 2(-4) Combine like terms: 20 + 12 = 32 32 + 10z + -4z = 3(z + -4) + 2(-4) Combine like terms: 10z + -4z = 6z 32 + 6z = 3(z + -4) + 2(-4) Reorder the terms: 32 + 6z = 3(-4 + z) + 2(-4) 32 + 6z = (-4 * 3 + z * 3) + 2(-4) 32 + 6z = (-12 + 3z) + 2(-4) Multiply 2 * -4 32 + 6z = -12 + 3z + -8 Reorder the terms: 32 + 6z = -12 + -8 + 3z Combine like terms: -12 + -8 = -20 32 + 6z = -20 + 3z Solving 32 + 6z = -20 + 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. 32 + 6z + -3z = -20 + 3z + -3z Combine like terms: 6z + -3z = 3z 32 + 3z = -20 + 3z + -3z Combine like terms: 3z + -3z = 0 32 + 3z = -20 + 0 32 + 3z = -20 Add '-32' to each side of the equation. 32 + -32 + 3z = -20 + -32 Combine like terms: 32 + -32 = 0 0 + 3z = -20 + -32 3z = -20 + -32 Combine like terms: -20 + -32 = -52 3z = -52 Divide each side by '3'. z = -17.33333333 Simplifying z = -17.33333333
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