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Simplifying 2z + 1 = 1 + 3z2 Reorder the terms: 1 + 2z = 1 + 3z2 Add '-1' to each side of the equation. 1 + -1 + 2z = 1 + -1 + 3z2 Combine like terms: 1 + -1 = 0 0 + 2z = 1 + -1 + 3z2 2z = 1 + -1 + 3z2 Combine like terms: 1 + -1 = 0 2z = 0 + 3z2 2z = 3z2 Solving 2z = 3z2 Solving for variable 'z'. Combine like terms: 3z2 + -3z2 = 0 2z + -3z2 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(2 + -3z) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {0, 0.6666666667}
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