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Simplifying 10(z + 4) + -4(z + -2) = 3(z + -1) + 2(-3) Reorder the terms: 10(4 + z) + -4(z + -2) = 3(z + -1) + 2(-3) (4 * 10 + z * 10) + -4(z + -2) = 3(z + -1) + 2(-3) (40 + 10z) + -4(z + -2) = 3(z + -1) + 2(-3) Reorder the terms: 40 + 10z + -4(-2 + z) = 3(z + -1) + 2(-3) 40 + 10z + (-2 * -4 + z * -4) = 3(z + -1) + 2(-3) 40 + 10z + (8 + -4z) = 3(z + -1) + 2(-3) Reorder the terms: 40 + 8 + 10z + -4z = 3(z + -1) + 2(-3) Combine like terms: 40 + 8 = 48 48 + 10z + -4z = 3(z + -1) + 2(-3) Combine like terms: 10z + -4z = 6z 48 + 6z = 3(z + -1) + 2(-3) Reorder the terms: 48 + 6z = 3(-1 + z) + 2(-3) 48 + 6z = (-1 * 3 + z * 3) + 2(-3) 48 + 6z = (-3 + 3z) + 2(-3) Multiply 2 * -3 48 + 6z = -3 + 3z + -6 Reorder the terms: 48 + 6z = -3 + -6 + 3z Combine like terms: -3 + -6 = -9 48 + 6z = -9 + 3z Solving 48 + 6z = -9 + 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. 48 + 6z + -3z = -9 + 3z + -3z Combine like terms: 6z + -3z = 3z 48 + 3z = -9 + 3z + -3z Combine like terms: 3z + -3z = 0 48 + 3z = -9 + 0 48 + 3z = -9 Add '-48' to each side of the equation. 48 + -48 + 3z = -9 + -48 Combine like terms: 48 + -48 = 0 0 + 3z = -9 + -48 3z = -9 + -48 Combine like terms: -9 + -48 = -57 3z = -57 Divide each side by '3'. z = -19 Simplifying z = -19
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