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Simplifying 5(4z + 6) + -2(z + -4) = 72(z + 4) + -2(72 + -2) + -48 Reorder the terms: 5(6 + 4z) + -2(z + -4) = 72(z + 4) + -2(72 + -2) + -48 (6 * 5 + 4z * 5) + -2(z + -4) = 72(z + 4) + -2(72 + -2) + -48 (30 + 20z) + -2(z + -4) = 72(z + 4) + -2(72 + -2) + -48 Reorder the terms: 30 + 20z + -2(-4 + z) = 72(z + 4) + -2(72 + -2) + -48 30 + 20z + (-4 * -2 + z * -2) = 72(z + 4) + -2(72 + -2) + -48 30 + 20z + (8 + -2z) = 72(z + 4) + -2(72 + -2) + -48 Reorder the terms: 30 + 8 + 20z + -2z = 72(z + 4) + -2(72 + -2) + -48 Combine like terms: 30 + 8 = 38 38 + 20z + -2z = 72(z + 4) + -2(72 + -2) + -48 Combine like terms: 20z + -2z = 18z 38 + 18z = 72(z + 4) + -2(72 + -2) + -48 Reorder the terms: 38 + 18z = 72(4 + z) + -2(72 + -2) + -48 38 + 18z = (4 * 72 + z * 72) + -2(72 + -2) + -48 38 + 18z = (288 + 72z) + -2(72 + -2) + -48 Combine like terms: 72 + -2 = 70 38 + 18z = 288 + 72z + -2(70) + -48 Multiply -2 * 70 38 + 18z = 288 + 72z + -140 + -48 Reorder the terms: 38 + 18z = 288 + -140 + -48 + 72z Combine like terms: 288 + -140 = 148 38 + 18z = 148 + -48 + 72z Combine like terms: 148 + -48 = 100 38 + 18z = 100 + 72z Solving 38 + 18z = 100 + 72z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-72z' to each side of the equation. 38 + 18z + -72z = 100 + 72z + -72z Combine like terms: 18z + -72z = -54z 38 + -54z = 100 + 72z + -72z Combine like terms: 72z + -72z = 0 38 + -54z = 100 + 0 38 + -54z = 100 Add '-38' to each side of the equation. 38 + -38 + -54z = 100 + -38 Combine like terms: 38 + -38 = 0 0 + -54z = 100 + -38 -54z = 100 + -38 Combine like terms: 100 + -38 = 62 -54z = 62 Divide each side by '-54'. z = -1.148148148 Simplifying z = -1.148148148
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