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Simplifying tan(3x + -4) = tan(5x + -8) Reorder the terms: ant(-4 + 3x) = tan(5x + -8) (-4 * ant + 3x * ant) = tan(5x + -8) (-4ant + 3antx) = tan(5x + -8) Reorder the terms: -4ant + 3antx = ant(-8 + 5x) -4ant + 3antx = (-8 * ant + 5x * ant) -4ant + 3antx = (-8ant + 5antx) Solving -4ant + 3antx = -8ant + 5antx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8ant' to each side of the equation. -4ant + 8ant + 3antx = -8ant + 8ant + 5antx Combine like terms: -4ant + 8ant = 4ant 4ant + 3antx = -8ant + 8ant + 5antx Combine like terms: -8ant + 8ant = 0 4ant + 3antx = 0 + 5antx 4ant + 3antx = 5antx Add '-5antx' to each side of the equation. 4ant + 3antx + -5antx = 5antx + -5antx Combine like terms: 3antx + -5antx = -2antx 4ant + -2antx = 5antx + -5antx Combine like terms: 5antx + -5antx = 0 4ant + -2antx = 0 Factor out the Greatest Common Factor (GCF), '2ant'. 2ant(2 + -1x) = 0 Ignore the factor 2.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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