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Simplifying tan(30 + x) = 2tan(60 + -1x) (30 * ant + x * ant) = 2tan(60 + -1x) (30ant + antx) = 2tan(60 + -1x) 30ant + antx = (60 * 2ant + -1x * 2ant) 30ant + antx = (120ant + -2antx) Solving 30ant + antx = 120ant + -2antx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-120ant' to each side of the equation. 30ant + -120ant + antx = 120ant + -120ant + -2antx Combine like terms: 30ant + -120ant = -90ant -90ant + antx = 120ant + -120ant + -2antx Combine like terms: 120ant + -120ant = 0 -90ant + antx = 0 + -2antx -90ant + antx = -2antx Add '2antx' to each side of the equation. -90ant + antx + 2antx = -2antx + 2antx Combine like terms: antx + 2antx = 3antx -90ant + 3antx = -2antx + 2antx Combine like terms: -2antx + 2antx = 0 -90ant + 3antx = 0 Factor out the Greatest Common Factor (GCF), '3ant'. 3ant(-30 + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'ant' equal to zero and attempt to solve: Simplifying ant = 0 Solving ant = 0 Move all terms containing a to the left, all other terms to the right. Simplifying ant = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Add '-1x' to each side of the equation. x + -1x = 30 + -1x Combine like terms: x + -1x = 0 0 = 30 + -1x Simplifying 0 = 30 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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