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Simplifying 5z + 7 = 6(z + -2) + -4(2z + -3) Reorder the terms: 7 + 5z = 6(z + -2) + -4(2z + -3) Reorder the terms: 7 + 5z = 6(-2 + z) + -4(2z + -3) 7 + 5z = (-2 * 6 + z * 6) + -4(2z + -3) 7 + 5z = (-12 + 6z) + -4(2z + -3) Reorder the terms: 7 + 5z = -12 + 6z + -4(-3 + 2z) 7 + 5z = -12 + 6z + (-3 * -4 + 2z * -4) 7 + 5z = -12 + 6z + (12 + -8z) Reorder the terms: 7 + 5z = -12 + 12 + 6z + -8z Combine like terms: -12 + 12 = 0 7 + 5z = 0 + 6z + -8z 7 + 5z = 6z + -8z Combine like terms: 6z + -8z = -2z 7 + 5z = -2z Solving 7 + 5z = -2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2z' to each side of the equation. 7 + 5z + 2z = -2z + 2z Combine like terms: 5z + 2z = 7z 7 + 7z = -2z + 2z Combine like terms: -2z + 2z = 0 7 + 7z = 0 Add '-7' to each side of the equation. 7 + -7 + 7z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7z = 0 + -7 7z = 0 + -7 Combine like terms: 0 + -7 = -7 7z = -7 Divide each side by '7'. z = -1 Simplifying z = -1
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