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Simplifying -7(z + -4) + -3z + 10 = 4(z + 3) + -1z Reorder the terms: -7(-4 + z) + -3z + 10 = 4(z + 3) + -1z (-4 * -7 + z * -7) + -3z + 10 = 4(z + 3) + -1z (28 + -7z) + -3z + 10 = 4(z + 3) + -1z Reorder the terms: 28 + 10 + -7z + -3z = 4(z + 3) + -1z Combine like terms: 28 + 10 = 38 38 + -7z + -3z = 4(z + 3) + -1z Combine like terms: -7z + -3z = -10z 38 + -10z = 4(z + 3) + -1z Reorder the terms: 38 + -10z = 4(3 + z) + -1z 38 + -10z = (3 * 4 + z * 4) + -1z 38 + -10z = (12 + 4z) + -1z Combine like terms: 4z + -1z = 3z 38 + -10z = 12 + 3z Solving 38 + -10z = 12 + 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. 38 + -10z + -3z = 12 + 3z + -3z Combine like terms: -10z + -3z = -13z 38 + -13z = 12 + 3z + -3z Combine like terms: 3z + -3z = 0 38 + -13z = 12 + 0 38 + -13z = 12 Add '-38' to each side of the equation. 38 + -38 + -13z = 12 + -38 Combine like terms: 38 + -38 = 0 0 + -13z = 12 + -38 -13z = 12 + -38 Combine like terms: 12 + -38 = -26 -13z = -26 Divide each side by '-13'. z = 2 Simplifying z = 2
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