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Simplifying -19(z + 3) + 6(4z + -7) = 4(z + -4) + 10 Reorder the terms: -19(3 + z) + 6(4z + -7) = 4(z + -4) + 10 (3 * -19 + z * -19) + 6(4z + -7) = 4(z + -4) + 10 (-57 + -19z) + 6(4z + -7) = 4(z + -4) + 10 Reorder the terms: -57 + -19z + 6(-7 + 4z) = 4(z + -4) + 10 -57 + -19z + (-7 * 6 + 4z * 6) = 4(z + -4) + 10 -57 + -19z + (-42 + 24z) = 4(z + -4) + 10 Reorder the terms: -57 + -42 + -19z + 24z = 4(z + -4) + 10 Combine like terms: -57 + -42 = -99 -99 + -19z + 24z = 4(z + -4) + 10 Combine like terms: -19z + 24z = 5z -99 + 5z = 4(z + -4) + 10 Reorder the terms: -99 + 5z = 4(-4 + z) + 10 -99 + 5z = (-4 * 4 + z * 4) + 10 -99 + 5z = (-16 + 4z) + 10 Reorder the terms: -99 + 5z = -16 + 10 + 4z Combine like terms: -16 + 10 = -6 -99 + 5z = -6 + 4z Solving -99 + 5z = -6 + 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. -99 + 5z + -4z = -6 + 4z + -4z Combine like terms: 5z + -4z = 1z -99 + 1z = -6 + 4z + -4z Combine like terms: 4z + -4z = 0 -99 + 1z = -6 + 0 -99 + 1z = -6 Add '99' to each side of the equation. -99 + 99 + 1z = -6 + 99 Combine like terms: -99 + 99 = 0 0 + 1z = -6 + 99 1z = -6 + 99 Combine like terms: -6 + 99 = 93 1z = 93 Divide each side by '1'. z = 93 Simplifying z = 93
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