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Simplifying lg(5x + -6) = 2lgx Reorder the terms: gl(-6 + 5x) = 2lgx (-6 * gl + 5x * gl) = 2lgx (-6gl + 5glx) = 2lgx Solving -6gl + 5glx = 2glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glx' to each side of the equation. -6gl + 5glx + -2glx = 2glx + -2glx Combine like terms: 5glx + -2glx = 3glx -6gl + 3glx = 2glx + -2glx Combine like terms: 2glx + -2glx = 0 -6gl + 3glx = 0 Factor out the Greatest Common Factor (GCF), '3gl'. 3gl(-2 + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 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 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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