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Simplifying 5(2z + -2) + -4(z + 2) = 3(z + 1) Reorder the terms: 5(-2 + 2z) + -4(z + 2) = 3(z + 1) (-2 * 5 + 2z * 5) + -4(z + 2) = 3(z + 1) (-10 + 10z) + -4(z + 2) = 3(z + 1) Reorder the terms: -10 + 10z + -4(2 + z) = 3(z + 1) -10 + 10z + (2 * -4 + z * -4) = 3(z + 1) -10 + 10z + (-8 + -4z) = 3(z + 1) Reorder the terms: -10 + -8 + 10z + -4z = 3(z + 1) Combine like terms: -10 + -8 = -18 -18 + 10z + -4z = 3(z + 1) Combine like terms: 10z + -4z = 6z -18 + 6z = 3(z + 1) Reorder the terms: -18 + 6z = 3(1 + z) -18 + 6z = (1 * 3 + z * 3) -18 + 6z = (3 + 3z) Solving -18 + 6z = 3 + 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. -18 + 6z + -3z = 3 + 3z + -3z Combine like terms: 6z + -3z = 3z -18 + 3z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -18 + 3z = 3 + 0 -18 + 3z = 3 Add '18' to each side of the equation. -18 + 18 + 3z = 3 + 18 Combine like terms: -18 + 18 = 0 0 + 3z = 3 + 18 3z = 3 + 18 Combine like terms: 3 + 18 = 21 3z = 21 Divide each side by '3'. z = 7 Simplifying z = 7
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