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Simplifying -8(z + 3) + 4(3z + -3) = 3(z + -5) + 1 Reorder the terms: -8(3 + z) + 4(3z + -3) = 3(z + -5) + 1 (3 * -8 + z * -8) + 4(3z + -3) = 3(z + -5) + 1 (-24 + -8z) + 4(3z + -3) = 3(z + -5) + 1 Reorder the terms: -24 + -8z + 4(-3 + 3z) = 3(z + -5) + 1 -24 + -8z + (-3 * 4 + 3z * 4) = 3(z + -5) + 1 -24 + -8z + (-12 + 12z) = 3(z + -5) + 1 Reorder the terms: -24 + -12 + -8z + 12z = 3(z + -5) + 1 Combine like terms: -24 + -12 = -36 -36 + -8z + 12z = 3(z + -5) + 1 Combine like terms: -8z + 12z = 4z -36 + 4z = 3(z + -5) + 1 Reorder the terms: -36 + 4z = 3(-5 + z) + 1 -36 + 4z = (-5 * 3 + z * 3) + 1 -36 + 4z = (-15 + 3z) + 1 Reorder the terms: -36 + 4z = -15 + 1 + 3z Combine like terms: -15 + 1 = -14 -36 + 4z = -14 + 3z Solving -36 + 4z = -14 + 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. -36 + 4z + -3z = -14 + 3z + -3z Combine like terms: 4z + -3z = 1z -36 + 1z = -14 + 3z + -3z Combine like terms: 3z + -3z = 0 -36 + 1z = -14 + 0 -36 + 1z = -14 Add '36' to each side of the equation. -36 + 36 + 1z = -14 + 36 Combine like terms: -36 + 36 = 0 0 + 1z = -14 + 36 1z = -14 + 36 Combine like terms: -14 + 36 = 22 1z = 22 Divide each side by '1'. z = 22 Simplifying z = 22
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