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Simplifying 3[5z + -7] + -2[9z + -11] = 4[8z + -13] + -17 Reorder the terms: 3[-7 + 5z] + -2[9z + -11] = 4[8z + -13] + -17 [-7 * 3 + 5z * 3] + -2[9z + -11] = 4[8z + -13] + -17 [-21 + 15z] + -2[9z + -11] = 4[8z + -13] + -17 Reorder the terms: -21 + 15z + -2[-11 + 9z] = 4[8z + -13] + -17 -21 + 15z + [-11 * -2 + 9z * -2] = 4[8z + -13] + -17 -21 + 15z + [22 + -18z] = 4[8z + -13] + -17 Reorder the terms: -21 + 22 + 15z + -18z = 4[8z + -13] + -17 Combine like terms: -21 + 22 = 1 1 + 15z + -18z = 4[8z + -13] + -17 Combine like terms: 15z + -18z = -3z 1 + -3z = 4[8z + -13] + -17 Reorder the terms: 1 + -3z = 4[-13 + 8z] + -17 1 + -3z = [-13 * 4 + 8z * 4] + -17 1 + -3z = [-52 + 32z] + -17 Reorder the terms: 1 + -3z = -52 + -17 + 32z Combine like terms: -52 + -17 = -69 1 + -3z = -69 + 32z Solving 1 + -3z = -69 + 32z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-32z' to each side of the equation. 1 + -3z + -32z = -69 + 32z + -32z Combine like terms: -3z + -32z = -35z 1 + -35z = -69 + 32z + -32z Combine like terms: 32z + -32z = 0 1 + -35z = -69 + 0 1 + -35z = -69 Add '-1' to each side of the equation. 1 + -1 + -35z = -69 + -1 Combine like terms: 1 + -1 = 0 0 + -35z = -69 + -1 -35z = -69 + -1 Combine like terms: -69 + -1 = -70 -35z = -70 Divide each side by '-35'. z = 2 Simplifying z = 2
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