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Simplifying -19(z + 2) + 6(4z + -6) = 4(z + -3) + 8 Reorder the terms: -19(2 + z) + 6(4z + -6) = 4(z + -3) + 8 (2 * -19 + z * -19) + 6(4z + -6) = 4(z + -3) + 8 (-38 + -19z) + 6(4z + -6) = 4(z + -3) + 8 Reorder the terms: -38 + -19z + 6(-6 + 4z) = 4(z + -3) + 8 -38 + -19z + (-6 * 6 + 4z * 6) = 4(z + -3) + 8 -38 + -19z + (-36 + 24z) = 4(z + -3) + 8 Reorder the terms: -38 + -36 + -19z + 24z = 4(z + -3) + 8 Combine like terms: -38 + -36 = -74 -74 + -19z + 24z = 4(z + -3) + 8 Combine like terms: -19z + 24z = 5z -74 + 5z = 4(z + -3) + 8 Reorder the terms: -74 + 5z = 4(-3 + z) + 8 -74 + 5z = (-3 * 4 + z * 4) + 8 -74 + 5z = (-12 + 4z) + 8 Reorder the terms: -74 + 5z = -12 + 8 + 4z Combine like terms: -12 + 8 = -4 -74 + 5z = -4 + 4z Solving -74 + 5z = -4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -74 + 5z + -4z = -4 + 4z + -4z Combine like terms: 5z + -4z = 1z -74 + 1z = -4 + 4z + -4z Combine like terms: 4z + -4z = 0 -74 + 1z = -4 + 0 -74 + 1z = -4 Add '74' to each side of the equation. -74 + 74 + 1z = -4 + 74 Combine like terms: -74 + 74 = 0 0 + 1z = -4 + 74 1z = -4 + 74 Combine like terms: -4 + 74 = 70 1z = 70 Divide each side by '1'. z = 70 Simplifying z = 70
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