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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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